PUTNAM INVESTMENT GRADE MUNICIPAL TRUST III
N-30D, 1997-12-29
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Putnam
Investment
Grade
Municipal
Trust III

ANNUAL REPORT
October 31, 1997

[LOGO: BOSTON * LONDON * TOKYO]



Fund highlights

* "As always, the fund invests across the spectrum of
   investment-grade bonds, but we have benefited particularly from our
   exposure to bonds in the lowest tier of the investment-grade sector."

                         --  Richard P. Wyke, manager
                             Putnam Investment Grade Municipal Trust III

* "[Municipal bond funds] are more liquid than actual munis. And you
   get access to a manager who may be able to play the credit-rating changes
   of a locality to your advantage." 

                         --  Fortune, August 18, 1997

   CONTENTS

 4 Report from Putnam Management

 8 Fund performance summary

11 Portfolio holdings

15 Financial statements

22 Results of October 9, 1997 shareholder meeting



From the Chairman

[GRAPHIC OMITTED: PHOTO OF GEORGE PUTNAM]

[copyright] Karsh, Ottawa

Dear Shareholder:

Against a backdrop of lingering concerns about the economy, interest rates,
and renewed inflation, the municipal bond market maintained a semblance of
stability during the 12 months ended October 31, 1997. 

Recognizing the fragility of this generally positive environment, Richard Wyke
pursued a slightly defensive policy in managing Putnam Investment Grade
Municipal Trust III during the period, which encompassed the fund's 1997
fiscal year. 

As he looks toward the months immediately ahead, Rick sees little reason to
waver from this course. In the report that follows, he provides more details
about the fiscal year's performance and provides some insights into what he
believes is in store for the months ahead.

Respectfully yours, 

/S/GEORGE PUTNAM
George Putnam
Chairman of the Trustees
December 17, 1997



Report from the Fund Manager 
Richard P. Wyke

Up until the last week of October 1997, when equity markets around the world
corrected, an atmosphere of low volatility and narrow trading ranges
characterized the fixed-income markets for most of the year. The lack of
direction stemmed from an ongoing tug of war between high economic growth
(negative for the bond market) and favorable low inflation news (positive for
the bond market).

Despite the subsequent narrow trading ranges for municipal bond prices, Putnam
Investment Grade Municipal Trust III produced outstanding returns of 9.31% at
net asset value and 15.54% at market price for the 12 months ended October 31,
1997. By comparison, the Lehman Brothers Municipal Bond Index posted a return
of 8.50% for the same period. Please see pages 8 and 9 for additional
performance information.

* CALIFORNIA AND NEW YORK PLAY KEY ROLES IN FUND PERFORMANCE

Through careful security selection and in-depth credit research, we have been
able to provide shareholders with an attractive level of monthly income. The
fund's investments in the California market offer an example of this
fundamental strategy at work. Although the state's recent fiscal past is
somewhat checkered, its improving economy has generated healthy tax revenues
and reduced the need for new bond issuance. As a result, relatively higher
demand for California municipal bonds has coincided with a decrease in supply.
Given this favorable environment, it is no surprise that California bonds have
outperformed the municipal market in general, and the fund's California
position has served it well.

Another example of prudent security selection appears in the fund's
investments in New York City bonds. Several years ago the Big Apple's problems
seemed overwhelming. Today it is apparent that the city has made dramatic
progress. Private sector employment is surging, the crime rate is down
dramatically, and the economy is thriving. The fund's bond holdings from New
York City reflect this optimism in the form of a steady income stream and
higher bond prices.

* SECTOR ALLOCATION ENHANCES RETURNS

By diversifying portfolio holdings across different states and industry
sectors, we seek to take advantage of opportunities while preserving a
relatively stable income stream. Airline-related holdings, which performed
well over the period, represented 18.7% of net assets. Once again the strong
economy has played an important role in improving the airline industry's
efforts to reduce costs and post record earnings. 

The fund's long-standing position in Denver City and County Airport revenue
bonds recently proved especially rewarding. The airport refunded some of its
outstanding bonds by investing the proceeds of a new bond issue in U.S.
government bonds that mature at the same time as the outstanding municipal
bonds. Because this refunding translates into added security for the bonds and
reduced credit risk, a boost in the bond's price is expected and an upgrade by
the rating agencies is likely to follow.

The health-care sector has been another source of strong performance for
municipal bond investors, reflecting the widespread consolidation taking place
in this industry. In an era of cost cutting and reform, this sector was
besieged with consolidations between nonprofit and for-profit institutions
during much of the year. However, the Justice Department's recent
investigation of Columbia Healthcare, a publicly traded company and active
buyer of hospitals, has slowed acquisition activity, thereby eliminating a
valuable catalyst for credit upgrades. Nevertheless, new issuance in this
sector has been low, providing a natural price support for existing
health-care bonds.

[GRAPHIC OMITTED: horizontal bar chart TOP INDUSTRY SECTORS]

TOP INDUSTRY SECTORS*

Hospitals/health care            26.4%

Transportation                   20.4%

Utilities                        14.0%

Water and sewerage               11.5%

Waste management                  5.0%

Footnote reads:
Based on net assets as of 10/31/97. Holdings will vary over time.

* FUND BENEFITS FROM QUALITY SPREAD COMPRESSION AND LOW CALL RISK

While your fund invests across the spectrum of investment-grade bonds, it
particularly benefited from its exposure to bonds in the lowest tier of the
investment-grade sector over this period. These bonds have continued to
outperform the higher-quality tiers, resulting in only a minimal price
difference between the two groups. This phenomenon, known as quality spread
compression, usually occurs during periods of strong economic growth such as
we have experienced. With interest rates relatively low and the strong economy
improving many issuers' financial positions, investors are more confident
about taking on extra risk and are rewarded with higher bond prices. 

Another way your fund's management team seeks to provide high and durable
returns is by improving call risk within the fund. Our goal is to enhance the
durability of the income stream by extending call dates on holdings. Callable
bonds carry the option of being redeemed or called away by the issuer at a
certain future date. Bonds are normally called away if interest rates are
lower than they were when the bonds were originally issued. By avoiding
callable bonds, we believe the portfolio has a better chance of maintaining a
certain level of income.

Throughout most of the year, as a result of relatively low interest rates, we
have seen many new and refunded issues coming to market. This overabundance of
supply held back municipal bond prices for a while until the October stock
market correction resulted in an explosive rally for fixed-income securities.
Since then, municipal bond yields have become extremely attractive relative to
taxable Treasuries and we have been taking full advantage of the resulting
opportunity.

[GRAPHIC OMITTED: pie chart PORTFOLIO QUALITY OVERVIEW]

PORTFOLIO QUALITY OVERVIEW*

Aaa                54.1%

Aa                  3.4%

A                  13.8%

Baa                25.6%

Ba                  3.1%

Footnote reads:
*As a percentage of portfolio market value on 10/31/97. A bond rated Baa or
higher is considered investment grade. All ratings reflect Moody's
terminologies and may include unrated bonds considered by Putnam Management to
be of comparable quality. Portfolio quality will vary over time.

* TAKING ADVANTAGE OF SHORT-TERM VOLATILITY TO ENHANCE RETURN

Since the Pacific Rim crisis and the subsequent correction in worldwide equity
markets, there has been enormous day-to-day volatility. Once the worldwide
equity markets settle down - a process that may take a few months - we expect
to return to a more typical municipal bond market. For the time being, it
appears that most markets have lost sight of the fundamental economic reasons
that typically cause extreme reactions. We realize that volatility can be
unsettling for investors, but as professional money managers, we can take
advantage of short-term distortions and use them to improve the fund's return
over time. 

As time goes on, however, we continue to believe there will be moderate upward
pressure on interest rates driven by the strong economy. We anticipate that
the news on inflation will slowly deteriorate. While keeping a vigilant eye on
the economy, we continue to rely on in-depth research to evaluate new and
existing holdings for the fund.

The views expressed here are exclusively those of Putnam Management. They are
not meant as investment advice. Although the described holdings were viewed
favorably as of 10/31/97, there is no guarantee the fund will continue to hold
these securities in the future. 



Performance summary

Performance should always be considered in light of a fund's investment
strategy. Putnam Investment Grade Municipal Trust III is designed for
investors seeking high current income free from federal income tax,
consistent with preservation of capital.

TOTAL RETURN FOR PERIODS ENDED 10/31/97

                                                        Lehman Bros.
                                              Market     Municipal
(common shares)                      NAV      price     Bond Index
- ---------------------------------------------------------------------
1 year                              9.31%     15.54%       8.50%
- ---------------------------------------------------------------------
Life of fund (11/29/93)             23.07     10.94       27.13
- ---------------------------------------------------------------------
Annual average                       5.44      2.68        6.32
- ---------------------------------------------------------------------

Performance data represent past results and do not reflect future
performance. They do not take into account any adjustment for taxes
payable on reinvested distributions. Investment returns, net asset value
and market price will fluctuate so that an investor's shares when sold may
be worth more or less than their original cost.

PRICE AND DISTRIBUTION INFORMATION
12 months ended 10/31/97

- ---------------------------------------------------------------------
Distributions (common shares)
- ---------------------------------------------------------------------
Number                                            12
- ---------------------------------------------------------------------
Income                                         $0.8004
- ---------------------------------------------------------------------
   Total                                       $0.8004
- ---------------------------------------------------------------------
Preferred shares Series A (200 shares)
- ---------------------------------------------------------------------
Income                                          $1,784.32
- ---------------------------------------------------------------------
   Total                                        $1,784.32
- ---------------------------------------------------------------------
Share value (common shares):             NAV          Market price
- ---------------------------------------------------------------------
10/31/96                              $13.02            $11.875
- ---------------------------------------------------------------------
10/31/97                               13.35             12.875
- ---------------------------------------------------------------------
Current return (common shares):          NAV          Market price
- ---------------------------------------------------------------------
End of period
- ---------------------------------------------------------------------
Current dividend rate1                  6.00%              6.22%
- ---------------------------------------------------------------------
Taxable equivalent2                     9.93              10.30
- ---------------------------------------------------------------------

1 Income portion of most recent distribution, annualized and divided by
  NAV or market price at end of period.

2 Assumes maximum 39.6% federal tax rate. Results for investors subject to
  lower tax rates would not be as advantageous.


TOTAL RETURN FOR PERIODS ENDED 9/30/97
(most recent calendar quarter)

                                                     Market
(common shares)                         NAV          price
- ---------------------------------------------------------------------
1 year                                 9.45%         14.30%
- ---------------------------------------------------------------------
Life of fund (11/29/93)               21.89          11.44
- ---------------------------------------------------------------------
Annual average                         5.29           2.86
- ---------------------------------------------------------------------

TERMS AND DEFINITIONS

Total return shows how the value of the fund's shares changed over time,
assuming you held the shares through the entire period and reinvested all
distributions in the fund.

Net asset value (NAV) is the value of all your fund's assets, minus any
liabilities and the net assets allocated to remarketed preferred shares,
divided by the number of outstanding common shares.

Market price is the current trading price of one share of the fund. Market
prices are set by transactions between buyers and sellers on the New York
Stock Exchange.

COMPARATIVE BENCHMARKS

Lehman Brothers Municipal Bond Index is an unmanaged list of long-term
fixed-rate investment-grade tax-exempt bonds representative of the
municipal bond market. The index assumes reinvestment of all distributions
and interest payments and does not take into account brokerage fees or
taxes. Securities in the fund do not match those in the indexes and
performance of the fund will differ. It is not possible to invest directly
in an index.

Consumer Price Index (CPI) is a commonly used measure of inflation; it
does not represent an investment return.



Report of independent accountants
For the fiscal year ended October 31, 1997

To the Trustees and Shareholders of 
Putnam Investment Grade Municipal Trust III

We have audited the accompanying statement of assets and liabilities of Putnam
Investment Grade Municipal Trust III, including the portfolio of investments
owned, as of October 31, 1997, and the related statement of operations for the
year then ended and the statements of changes in net assets for each of the
two years in the period then ended, and the financial highlights for each of
the periods indicated therein. These financial statements and financial
highlights are the responsibility of the fund's management. Our responsibility
is to express an opinion on these financial statements and financial
highlights based on our audits. 

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures in
the financial statements. Our procedures included confirmation of securities
owned as of October 31, 1997, by correspondence with the custodian and
brokers. An audit also includes assessing the accounting principles used and
significant estimates made by management, as well as evaluating the overall
financial statement presentation. We believe that our audits provide a
reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of
Putnam Investment Grade Municipal Trust III as of October 31, 1997, the
results of its operations for the year then ended and the changes in its net
assets for each of the two years in the period then ended and the financial
highlights for each of the periods indicated therein, in conformity with
generally accepted accounting principles.

                                                 Coopers & Lybrand L.L.P
Boston, Massachusetts
December 10, 1997




<TABLE>
<CAPTION>

Portfolio of investments owned
October 31, 1997 

Key to Abbreviations
AMBAC        - AMBAC Indemnity Corporation
FGIC         - Financial Guaranty Insurance Company
FSA          - Financial Security Assurance
G.O. Bonds   - General Obligation Bonds
IFB          - Inverse Floating Rate Bonds
IF COP       - Inverse Floating Rate Certificate of Participation
MBIA         - Municipal Bond Investors Assurance Corporation


MUNICIPAL BONDS AND NOTES (96.5%) *
PRINCIPAL AMOUNT                                                               RATING**               VALUE

California (14.9%)
 <S>             <C>                                                           <C>             <C>
- ------------------------------------------------------------------------------------------------------------
     $2,500,000  Beverly Hills, Pub. Fin. Auth. Lease Rev. Bonds,
                   MBIA, 5.65s, 6/1/15                                         Aaa               $ 2,568,750
      2,000,000  CA Poll. Control Fin. Auth. Rev. Bonds
                   (San Diego Gas & Elec.), Ser. A, 5.9s, 6/1/14               A2                  2,162,500
      1,250,000  CA State U. IFB, AMBAC, 10.224s, 11/1/21
                   (acquired 9/2/94, cost $1,339,094) [DBL. DAGGERS]           Aaa                 1,489,063
      1,000,000  Central Coast Wtr. Auth. Rev. Bonds (State Wtr.
                   Regl. Fac.), Ser. A, AMBAC, 5s, 10/1/13                     Aaa                   991,250
      1,500,000  Foothill/Eastern Trans. Corridor Agcy. Toll Rd.
                   Rev. Bonds, Sr. Lien, Ser. A, zero %, 1/1/08                Baa                 1,061,250
      1,000,000  San Diego Cnty., Wtr. Auth. IF COP, FGIC,
                   7.535s, 4/23/08 #                                           Aaa                 1,185,000
                                                                                                ------------
                                                                                                   9,457,813

Colorado (14.9%)
- ------------------------------------------------------------------------------------------------------------
                 Denver, City & Cnty. Arpt. Rev. Bonds
      2,205,000    Ser. A, 8 3/4s, 11/15/23                                    Baa1                2,590,875
        795,000    Prerefunded, Ser. A, 8 3/4s, 11/15/23                       Baa1                  936,113
      1,370,000    Ser. A, 8 1/2s, 11/15/23                                    Baa1                1,541,250
        130,000    Prerefunded, Ser. A, 8 1/2s, 11/15/23                       Baa1                  147,388
      1,000,000    Ser. D, 7 3/4s, 11/15/13                                    Baa1                1,245,000
      3,000,000    Ser. A, MBIA, 5 1/2s, 11/15/25                              Aaa                 3,003,750
                                                                                                ------------
                                                                                                   9,464,376

Florida (5.0%)
- ------------------------------------------------------------------------------------------------------------
                 Broward Cnty., Resource Recvy. Rev. Bonds
        965,000    (SES Broward Cnty. LP South), 7.95s, 12/1/08 #              A                   1,051,850
      1,965,000    (Waste-Energy LP North), 7.95s, 12/1/08 #                   A                   2,141,850
                                                                                                ------------
                                                                                                   3,193,700

Georgia (2.2%)
- ------------------------------------------------------------------------------------------------------------
      1,250,000  GA Muni. Elec. Auth. Rev. Bonds Special Obligation
                   Bonds (Crossover Ser.), AMBAC, 6.4s, 1/1/13                 Aaa                 1,429,688

Illinois (6.5%)
- ------------------------------------------------------------------------------------------------------------
                 IL Hlth. Fac. Auth. Rev. Bonds
      1,760,000    (Glenoaks Med. Ctr.), Ser. D, 9 1/2s, 11/15/15              Baa1                2,046,000
      2,000,000    (Highland Pk. Hosp.), Ser. A, MBIA,
                   5 3/4s, 10/1/17                                             Aaa                 2,065,000
                                                                                                ------------
                                                                                                   4,111,000

Indiana (3.4%)
- ------------------------------------------------------------------------------------------------------------
      2,000,000  Marion Cnty., Ind. Convention & Recreation Fac.
                   Auth. Rev. Bonds (Excise Tax Rev. Lease Rental),
                   Ser. A, AMBAC, 7s, 6/1/21                                   Aaa                 2,185,000

Kansas (4.2%)
- ------------------------------------------------------------------------------------------------------------
      2,400,000  Burlington, Poll. Control Rev. Bonds
                   (Kansas Gas & Elec. Co.), MBIA, 7s, 6/1/31                  Aaa                 2,640,000

Louisiana (2.5%)
- ------------------------------------------------------------------------------------------------------------
      1,420,000  Beauregard, Parish Rev. Bonds
                   (Boise Cascade Corp.), 7 3/4s, 6/1/21                       Baa3                1,577,975

Maryland (3.3%)
- ------------------------------------------------------------------------------------------------------------
      2,000,000  MD State Hlth. & Higher Edl. Fac. Auth. Rev. Bonds
                   (Johns Hopkins U.), 7 1/2s, 7/1/20                          Aa2                 2,079,920

Massachusetts (5.4%)
- ------------------------------------------------------------------------------------------------------------
        750,000  MA State Hlth. & Edl. Fac. Auth. IFB (Med. Ctr. of
                   Central MA), Ser. B, AMBAC, 9.02s, 6/23/22                  Aaa                   935,625
      1,000,000  MA State Hsg. Fin. Agcy. Rev. Bonds, Ser. 53, MBIA,
                   6.15s, 12/1/29                                              Aaa                 1,047,500
        830,000  MA State Port Auth. Rev. Bonds, 13s, 7/1/13                   Aaa                 1,419,300
                                                                                               ------------
                                                                                                   3,402,425

Michigan (1.6%)
- ------------------------------------------------------------------------------------------------------------
      1,000,000  MI State Hosp. Fin. Auth. Rev. Bonds
                   (Pontiac Osteopathic Hosp.), Ser. A, 6s, 2/1/24             Baa1                1,015,000

Minnesota (5.4%)
- ------------------------------------------------------------------------------------------------------------
        925,000  SCA Multi-Fam. Mtge. Rev. Bonds (Burnsville),
                   Ser. A-9, FSA, 7.1s, 1/1/30                                 Aaa                 1,029,063
                 St. Paul, Hsg. & Hosp. Redev. Auth. Rev. Bonds
                   (Healtheast), Ser. B
      1,000,000    9 3/4s, 11/1/17                                             Baa3                1,023,750
      1,375,000    9 5/8s, 11/1/08                                             Baa3                1,407,656
                                                                                                ------------
                                                                                                   3,460,469

New Jersey (2.9%)
- ------------------------------------------------------------------------------------------------------------
      1,745,000  NJ Hlth. Care Fac. Fin. Auth. Rev. Bonds
                   (Newcomb Med. Ctr.), Ser. A, 7 7/8s, 7/1/03                 Ba3                 1,869,331

New York (11.8%)
- ------------------------------------------------------------------------------------------------------------
      1,000,000  Metropolitan Trans. Auth. Commuter Fac.
                   Rev. Bonds, Ser. A, MBIA, 5 5/8s, 7/1/27                    Aaa               $ 1,018,750
      1,000,000  NY City, G.O. Bonds, Ser. B, 7 1/2s, 2/1/06                   Baa1                1,117,500
                 NY City, Muni. Wtr. & Swr. Syst. Fin. Auth. Rev. Bonds
      2,000,000    Ser. C, 7 3/4s, 6/15/20                                     AAA                 2,267,500
      1,000,000    Ser. B, 5 3/4s, 6/15/26                                     A2                  1,023,750
                 NY State Energy Research & Dev. Auth. Elec. Fac.
                   Rev. Bonds (Cons. Edison Co. of NY, Inc.), Ser. A
      1,000,000    7 3/4s, 1/1/24                                              A1                  1,020,500
      1,000,000    7 1/2s, 1/1/26                                              A1                  1,072,500
                                                                                                ------------
                                                                                                   7,520,500

Puerto Rico (0.9%)
- ------------------------------------------------------------------------------------------------------------
        500,000  PR Elec. Pwr. Auth. IFB, FSA, 8.208s, 7/1/23                  Aaa                   547,500

Tennessee (4.8%)
- ------------------------------------------------------------------------------------------------------------
      2,700,000  Metropolitan Govt. Nashville & Davidson Cnty.,
                   Tenn. Wtr. & Swr. IFB, AMBAC, 8.276s, 1/1/22                Aaa                 3,034,125

Texas (6.8%)
- ------------------------------------------------------------------------------------------------------------
      2,400,000  Bexar Cnty., Hlth. Fac. Dev. Corp. Rev. Bonds
                   (St. Luke's Lutheran Hosp.), 7.9s, 5/1/18                   AAA/P               2,805,000
      1,250,000  North Central Hlth. Fac. Dev. Corp. IFB
                   (Presbyterian Hlth. Care Syst.), Ser. C, MBIA,
                   9.425s, 6/15/21                                             Aaa                 1,492,186
                                                                                                ------------
                                                                                                   4,297,186
- ------------------------------------------------------------------------------------------------------------
                 Total Investments (cost $58,864,494) ***                                         61,286,008
- ------------------------------------------------------------------------------------------------------------

            * Percentages indicated are based on net assets of $63,498,373. 

           ** The Moody's or Standard & Poor's ratings indicated are
              believed to be the most recent ratings available at October 31, 1997 for the
              securities listed. Ratings are generally ascribed to securities at the
              time of issuance. While the agencies may from time to time revise such
              ratings, they undertake no obligation to do so, and the ratings do not
              necessarily represent what the agencies would ascribe to these
              securities at October 31, 1997. Securities rated by Putnam are indicated
              by "/P" and are not publicly rated. Ratings are not covered by the
              Report of independent accountants. 

          *** The aggregate identified cost on a tax basis is $58,935,758,
              resulting in gross unrealized appreciation and depreciation of
              $2,800,665 and $450,415, respectively, or net unrealized appreciation of
              $2,350,250. 

            # A portion of these securities was pledged and segregated with
              the custodian to cover margin requirements for futures contracts at
              October 31, 1997. 

[DBL. DAGGER] Restricted, excluding 144A securities, as to public resale. The
              total market value of restricted securities held at October 31, 1997 was
              $1,489,063 or 2.3% of net assets. 

             The rates shown on IFB and IF COP, which are securities paying
             interest rates that vary inversely to changes in the market interest
             rates, are the current interest rates at October 31, 1997. 

             The fund had the following industry group concentrations greater
             than 10% at October 31, 1997 (as a percentage of net assets): 

                Hospitals/Health care        26.4% 
                Transportation               20.4 
                Utilities                    14.0 
                Water & sewerage             11.5 

             The fund had the following insurance concentrations greater than
             10% at October 31, 1997 (as a percentage of net assets): 

                MBIA                         21.8% 
                AMBAC                        15.9 

</TABLE>



<TABLE>
<CAPTION>

- ---------------------------------------------------------------------------------------------------
Futures Contracts Outstanding at October 31, 1997
                                  Total      Aggregate Face      Expiration         Unrealized
                                   Value          Value             Date            Appreciation
- ---------------------------------------------------------------------------------------------------
<S>                               <C>            <C>              <C>               <C>
Municipal Index
Future (long)                      $7,310,625      7,146,563        Dec-97           $164,062
- ---------------------------------------------------------------------------------------------------

</TABLE>



<TABLE>
<CAPTION>

Statement of assets and liabilities
October 31, 1997

<S>                                                                                   <C>
Assets
- ---------------------------------------------------------------------------------------------------
Investments in securities, at value
(identified cost $58,864,494) (Note 1)                                                  $61,286,008
- ---------------------------------------------------------------------------------------------------
Cash                                                                                      1,005,704
- ---------------------------------------------------------------------------------------------------
Interest receivable                                                                       1,478,361
- ---------------------------------------------------------------------------------------------------
Receivable for securities sold                                                              135,000
- ---------------------------------------------------------------------------------------------------
Receivable for variation margin                                                               7,500
- ---------------------------------------------------------------------------------------------------
Unamortized organization expenses (Note 1)                                                    6,285
- ---------------------------------------------------------------------------------------------------
Total assets                                                                            $63,918,858

Liabilities
- ---------------------------------------------------------------------------------------------------
Distributions payable to shareholders                                                       267,258
- ---------------------------------------------------------------------------------------------------
Payable for compensation of Manager (Note 2)                                                113,700
- ---------------------------------------------------------------------------------------------------
Payable for investor servicing and custodian fees (Note 2)                                    4,949
- ---------------------------------------------------------------------------------------------------
Payable for compensation of Trustees (Note 2)                                                 5,901
- ---------------------------------------------------------------------------------------------------
Payable for administrative services (Note 2)                                                    362
- ---------------------------------------------------------------------------------------------------
Other accrued expenses                                                                       28,315
- ---------------------------------------------------------------------------------------------------
Total liabilities                                                                           420,485
- ---------------------------------------------------------------------------------------------------
Net assets                                                                              $63,498,373

Represented by
- ---------------------------------------------------------------------------------------------------
Series A remarketed preferred shares (200 shares issued and
outstanding at $50,000 per share) (Note 4)                                               10,000,000
- ---------------------------------------------------------------------------------------------------
Paid-in capital -- common shares (unlimited shares authorized) (Note 1)                  55,817,870
- ---------------------------------------------------------------------------------------------------
Undistributed net investment income (Note 1)                                                159,930
- ---------------------------------------------------------------------------------------------------
Accumulated net realized loss on investments (Note 1)                                    (5,065,003)
- ---------------------------------------------------------------------------------------------------
Net unrealized appreciation of investments                                                2,585,576
- ---------------------------------------------------------------------------------------------------
Total -- Representing net assets applicable to
capital shares outstanding                                                              $63,498,373

Computation of net asset value
- ---------------------------------------------------------------------------------------------------
Series A remarketed preferred shares                                                    $10,000,000
- ---------------------------------------------------------------------------------------------------
Cumulative undeclared dividends on remarketed preferred shares                               14,795
- ---------------------------------------------------------------------------------------------------
Net assets allocated to remarketed preferred shares --
liquidation preference                                                                  $10,014,795
- ---------------------------------------------------------------------------------------------------
Net assets available to common shares                                                   $53,483,578
- ---------------------------------------------------------------------------------------------------
Net asset value per common share
($53,483,578 divided by 4,007,092 shares)                                                    $13.35
- ---------------------------------------------------------------------------------------------------

The accompanying notes are an integral part of these financial statements.

</TABLE>




<TABLE>
<CAPTION>

Statement of operations
Year ended October 31, 1997

<S>                                                                                    <C>
Tax exempt interest income:                                                             $4,103,070
- --------------------------------------------------------------------------------------------------

Expenses:
- --------------------------------------------------------------------------------------------------
Compensation of Manager (Note 2)                                                           437,924
- --------------------------------------------------------------------------------------------------
Investor servicing and custodian fees (Note 2)                                              61,717
- --------------------------------------------------------------------------------------------------
Compensation of Trustees (Note 2)                                                           12,830
- --------------------------------------------------------------------------------------------------
Administrative services (Note 2)                                                             4,423
- --------------------------------------------------------------------------------------------------
Reports to shareholders                                                                     15,473
- --------------------------------------------------------------------------------------------------
Auditing                                                                                    48,061
- --------------------------------------------------------------------------------------------------
Legal                                                                                       11,616
- --------------------------------------------------------------------------------------------------
Postage                                                                                      8,089
- --------------------------------------------------------------------------------------------------
Exchange listing fees                                                                        3,333
- --------------------------------------------------------------------------------------------------
Amortization of organization expenses (Note 1)                                               4,984
- --------------------------------------------------------------------------------------------------
Preferred share remarketing agent fees                                                      25,000
- --------------------------------------------------------------------------------------------------
Other                                                                                       49,445
- --------------------------------------------------------------------------------------------------
Total expenses                                                                             682,895
- --------------------------------------------------------------------------------------------------
Expense reduction (Note 2)                                                                 (38,094)
- --------------------------------------------------------------------------------------------------
Net expenses                                                                               644,801
- --------------------------------------------------------------------------------------------------
Net investment income                                                                    3,458,269
- --------------------------------------------------------------------------------------------------
Net realized loss on investments (Notes 1 and 3)                                          (126,314)
- --------------------------------------------------------------------------------------------------
Net realized gain on futures contracts (Note 1)                                             15,556
- --------------------------------------------------------------------------------------------------
Net unrealized appreciation of investments and
futures during the year                                                                  1,548,774
- --------------------------------------------------------------------------------------------------
Net gain on investments                                                                  1,438,016
- --------------------------------------------------------------------------------------------------
Net increase in net assets resulting from operations                                    $4,896,285
- --------------------------------------------------------------------------------------------------

The accompanying notes are an integral part of these financial statements.

</TABLE>




<TABLE>
<CAPTION>

Statement of changes in net assets
 
                                                                                               Year ended October 31
                                                                                      --------------------------------
                                                                                               1997               1996
- ----------------------------------------------------------------------------------------------------------------------
<S>                                                                                   <C>                <C>
Increase (decrease) in net assets
- ----------------------------------------------------------------------------------------------------------------------
Operations:
- ----------------------------------------------------------------------------------------------------------------------
Net investment income                                                                   $ 3,458,269        $ 3,297,331
- ----------------------------------------------------------------------------------------------------------------------
Net realized loss on investments                                                           (110,758)          (280,731)
- ----------------------------------------------------------------------------------------------------------------------
Net unrealized appreciation (depreciation) of investments                                 1,548,774           (268,149)
- ----------------------------------------------------------------------------------------------------------------------
Net increase in net assets resulting from operations                                      4,896,285          2,748,451
- ----------------------------------------------------------------------------------------------------------------------
Distributions to remarketed preferred shareholders:
- ----------------------------------------------------------------------------------------------------------------------
From net investment income                                                                 (356,863)          (360,126)
- ----------------------------------------------------------------------------------------------------------------------
Net increase in net assets resulting from operations
applicable to common shareholders (excluding cumulative
undeclared dividends on remarketed preferred shares
of $14,795 and $13,233, respectively)                                                     4,539,422          2,388,325
- ----------------------------------------------------------------------------------------------------------------------
Distributions to common shareholders:
- ----------------------------------------------------------------------------------------------------------------------
From net investment income                                                               (3,207,038)        (3,207,079)
- ----------------------------------------------------------------------------------------------------------------------
Total increase (decrease) in net assets                                                   1,332,384           (818,754)

Net assets
- ----------------------------------------------------------------------------------------------------------------------
Beginning of year                                                                        62,165,989         62,984,743
- ----------------------------------------------------------------------------------------------------------------------
End of year (including undistributed net investment income
of $159,930 and $266,215, respectively)                                                 $63,498,373        $62,165,989
- ----------------------------------------------------------------------------------------------------------------------

Number of fund shares
- ----------------------------------------------------------------------------------------------------------------------
Common shares outstanding at beginning and end of year                                    4,007,092          4,007,092
- ----------------------------------------------------------------------------------------------------------------------
Remarketed preferred shares outstanding at
beginning and end of year                                                                       200                200
- ----------------------------------------------------------------------------------------------------------------------

The accompanying notes are an integral part of these financial statements.

</TABLE>



<TABLE>
<CAPTION>
Financial highlights
(For a share outstanding throughout the period)

- ------------------------------------------------------------------------------------------------------------------------------------

                                                                                                                   For the period
Per-share                                                                                                          Nov. 29, 1993+
operating performance                                                          Year ended October 31               to October 31
- ------------------------------------------------------------------------------------------------------------------------------------
                                                                      1997             1996             1995             1994
- ------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                <C>              <C>              <C>              <C>
Net asset value,
beginning of period
(common shares)                                                     $13.02           $13.22           $12.36           $14.02(a)
- ------------------------------------------------------------------------------------------------------------------------------------
Investment operations
- ------------------------------------------------------------------------------------------------------------------------------------
Net investment income                                                  .86              .82              .90              .85(c)
- ------------------------------------------------------------------------------------------------------------------------------------
Net realized and unrealized
gain (loss) on investments                                             .36             (.13)             .85            (1.69)
- ------------------------------------------------------------------------------------------------------------------------------------
Total from
investment operations                                                 1.22              .69             1.75             (.84)
- ------------------------------------------------------------------------------------------------------------------------------------
Less distributions:
- ------------------------------------------------------------------------------------------------------------------------------------
From net
investment income
- ------------------------------------------------------------------------------------------------------------------------------------
To preferred shareholders                                             (.09)            (.09)            (.09)            (.06)(b)
- ------------------------------------------------------------------------------------------------------------------------------------
To common shareholders                                                (.80)            (.80)            (.80)            (.67)
- ------------------------------------------------------------------------------------------------------------------------------------
Total distributions:                                                  (.89)            (.89)            (.89)            (.73)
- ------------------------------------------------------------------------------------------------------------------------------------
Preferred share
offering costs                                                          --               --               --             (.09)
- ------------------------------------------------------------------------------------------------------------------------------------
Net asset value,
end of period
(common shares)                                                     $13.35           $13.02           $13.22           $12.36
- ------------------------------------------------------------------------------------------------------------------------------------
Market value,
end of period
(common shares)                                                    $12.875          $11.875          $11.875          $10.125
- ------------------------------------------------------------------------------------------------------------------------------------
Ratios and supplemental data
- ------------------------------------------------------------------------------------------------------------------------------------
Total investment return
at market value
(common shares) (%)(d)                                               15.54             6.89            25.77           (28.60)*
- ------------------------------------------------------------------------------------------------------------------------------------
Net assets, end of period
(total fund) (in thousands)                                        $63,498          $62,166          $62,985          $59,518
- ------------------------------------------------------------------------------------------------------------------------------------
Ratio of expenses to
average net assets (%)(e)(f)                                          1.30             1.30             1.23              .85(c)*
- ------------------------------------------------------------------------------------------------------------------------------------
Ratio of net investment income
to average net assets (%)(e)                                          5.90             5.59             6.30             5.89(c)*
- ------------------------------------------------------------------------------------------------------------------------------------
Portfolio turnover rate (%)                                          37.75           123.89           165.21           148.90*
- ------------------------------------------------------------------------------------------------------------------------------------

  + Commencement of operations.

  * Not annualized.

(a) Represents initial net asset value of $14.10 less offering expenses of $0.08. Of these expenses $0.02
    are due to a revision of offering expenses on August 31, 1994.

(b) Preferred shares were issued on February 10, 1994. (Note 4)

(c) Reflects an expense limitation in effect during the period. As a result of such limitation, expenses of
    the fund for the period reflect a reduction of $0.02 per share.

(d) Total investment return assumes dividend reinvestment.

(e) Ratios reflect net assets available to common shares only; net investment income ratio also reflects
    reduction for dividend payments to preferred shareholders.

(f) The ratio of expenses to average net assets for the year ended October 31, 1995 and thereafter
    includes amounts paid through expense offset arrangements. Prior period ratios exclude
    these amounts. (Note 2)

</TABLE>



Notes to financial statements
October 31, 1997

Note 1 
Significant accounting policies

Putnam Investment Grade Municipal Trust III, (the "fund") is registered under
the Investment Company Act of 1940, as amended, as a diversified, closed-end
management investment company. The fund's investment objective is to provide
as high a level of current income exempt from federal income tax as is
believed to be consistent with preservation of capital. The fund intends to
achieve its objective by investing in a diversified portfolio of investment
grade municipal securities that Putnam Investment Management, Inc. ("Putnam
Management"), the fund's Manager, a wholly-owned subsidiary of Putnam
Investments, Inc., believes does not involve undue risk to income or
principal.

The following is a summary of significant accounting policies consistently
followed by the fund in the preparation of its financial statements. The
preparation of financial statements is in conformity with generally accepted
accounting principles and requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities. Actual
results could differ from those estimates.

A) Security valuation Tax-exempt bonds and notes are stated on the basis of
valuations provided by a pricing service, approved by the Trustees, which uses
information with respect to transactions in bonds, quotations from bond
dealers, market transactions in comparable securities and various
relationships between securities in determining value. The fair market value
of restricted securities is determined by Putnam Management following
procedures approved by the Trustees, and such valuations and procedures are
reviewed periodically by the Trustees.

B) Security transactions and related investment income Security transactions
are accounted for on the trade date (date the order to buy or sell is
executed). Interest income is recorded on the accrual basis.

C) Futures and options contracts The fund may use futures and options
contracts to hedge against changes in the values of securities the fund owns
or expects to purchase. The fund may also write options on securities it owns
or in which it may invest to increase its current returns.

The potential risk to the fund is that the change in value of futures and
options contracts may not correspond to the change in value of the hedged
instruments. In addition, losses may arise from changes in the value of the
underlying instruments, if there is an illiquid secondary market for the
contracts, or if the counterparty to the contract is unable to perform.

Futures contracts are valued at the quoted daily settlement prices established
by the exchange on which they trade. Exchange traded options are valued at the
last sale price, or if no sales are reported, the last bid price for purchased
options and the last ask price for written options. Options traded
over-the-counter are valued using prices supplied by dealers.

D) Federal taxes It is the policy of the fund to distribute all of its income
within the prescribed time and otherwise comply with the provisions of the
Internal Revenue Code applicable to regulated investment companies. It is also
the intention of the fund to distribute an amount sufficient to avoid
imposition of any excise tax under Section 4982 of the Internal Revenue Code
of 1986, as amended. Therefore, no provision has been made for federal taxes
on income, capital gains or unrealized appreciation on securities held nor for
excise tax on income and capital gains.

At October 31, 1997, the fund had a capital loss carryover of approximately
$4,470,000 available to offset future capital gains, if any. The amount of the
carryover and the expiration dates are:

Loss Carryover          Expiration
- ---------------   --------------------
  $1,911,000       October 31, 2002
   1,863,000       October 31, 2003
     452,000       October 31, 2004
     244,000       October 31, 2005

E) Distributions to shareholders Distributions to common and preferred
shareholders are recorded by the fund on the ex-dividend date. Dividends on
remarketed preferred shares become payable when, as and if declared by the
Trustees. Each dividend period for the remarketed preferred shares is
generally a 28 day period. The applicable dividend rate for the remarketed
preferred shares on October 31, 1997 was 3.60%. The amount and character of
income and gains to be distributed are determined in accordance with income
tax regulations which may differ from generally accepted accounting
principles. Reclassifications are made to the fund's capital accounts to
reflect income and gains available for distribution (or available capital loss
carryovers) under income tax regulations. For the year ended November 30,
1997, the fund reclassified $653 to decrease undistributed net investment
income and $653 to increase paid-in-capital. The calculation of net investment
income per share in the financial highlights table excludes these adjustments.

F) Determination of net asset value Net asset value of the common shares is
determined by dividing the value of all assets of the fund, less all
liabilities and the liquidation preference of any outstanding remarketed
preferred shares, by the total number of common shares outstanding.

G) Amortization of bond premium and accretion of bond discount Any premium
resulting from the purchase of securities in excess of maturity value is
amortized on a yield-to-maturity basis. Discounts on zero coupon bonds and
original issue discount bonds are accreted according to the effective yield
method.

H) Unamortized organization expenses Expenses incurred by the fund in
connection with its organization, its registration with the Securities and
Exchange Commission and with various states and the initial public offering of
its shares were $27,157. These expenses are being amortized on a straight-line
basis over a five-year period.

Note 2
Management fee,
administrative services 
and other transactions

Compensation of Putnam Management, for management and investment advisory
services is paid quarterly based on the average net assets of the fund. Such
fee is based on the following annual rates: 0.70% of the first $500 million of
the average net asset value of the fund, 0.60% of the next $500 million, 0.55%
of the next $500 million, and 0.50% of any amount over $1.5 billion.

If dividends payable on remarketed preferred shares during any dividend
payment period plus any expenses attributable to remarketed preferred shares
for that period exceed the fund's net income attributable to the proceeds of
the remarketed preferred shares during that period, then the fee payable to
Putnam Management for that period will be reduced by the amount of the excess
(but not more than .70% of the liquidation preference of the remarketed
preferred shares outstanding during the period).

The fund reimburses Putnam Management for the compensation and related
expenses of certain officers of the fund and their staff who provide
administrative services to the fund. The aggregate amount of all such
reimbursements is determined annually by the Trustees.

Custodial functions for the fund's assets are provided by Putnam Fiduciary
Trust Company (PFTC), a wholly-owned subsidiary of Putnam Investments, Inc.
Investor servicing agent functions are provided by Putnam Investor Services, a
division of PFTC.

For the year ended October 31, 1997, fund expenses were reduced by $38,094
under expense offset arrangements with PFTC. Investor servicing and custodian
fees reported in the Statement of operations exclude these credits. The fund
could have invested a portion of the assets utilized in connection with the
expense offset arrangements in an income producing asset if it had not entered
into such arrangements.

Trustees of the fund receive an annual Trustees fee of $444 and an additional
fee for each Trustee's meeting attended. Trustees who are not interested
persons of Putnam Management and who serve on committees of the Trustees
receive additional fees for attendance at certain committee meetings.

The fund has adopted a Trustee Fee Deferral Plan (the "Deferral Plan") which
allows the Trustees to defer the receipt of all or a portion of Trustees Fees
payable on or after July 1, 1995. The deferred fees remain in the fund and are
invested in certain Putnam funds until distribution in accordance with the
Deferral Plan.

The fund has adopted an unfunded noncontributory defined benefit pension plan
(the "Pension Plan") covering all Trustees of the fund who have served as
Trustee for at least five years. Benefits under the Pension Plan are equal to
50% of the Trustee's average total retainer and meeting fees for the three
years preceding retirement. Pension expense for the fund is included in
Compensation of trustees in the Statement of operations. Accrued pension
liability is included in Payable for compensation of Trustees in the Statement
of assets and liabilities.

Note 3
Purchase and sales of securities

During the year ended October 31, 1997, purchases and sales of investment
securities other than short-term investments aggregated $23,117,962 and
$25,535,057, respectively. There were no purchases and sales of U.S.
government obligations. In determining the net gain or loss on securities
sold, the cost of securities has been determined on the identified cost basis.

Note 4 
Remarketed preferred shares

The remarketed preferred shares are redeemable at the option of the fund on
any dividend payment date at a redemption price of $50,000 per share, plus an
amount equal to any dividends accumulated on a daily basis but unpaid through
the redemption date (whether or not such dividends have been declared) and, in
certain circumstances, a call premium.

It is anticipated that dividends paid to holders of remarketed preferred
shares will be considered tax-exempt dividends under the Internal Revenue Code
of 1986. To the extent that the fund earns taxable income and capital gains by
the conclusion of a fiscal year, it will be required to apportion to the
holders of the remarketed preferred shares throughout that year additional
dividends as necessary to result in an after-tax equivalent to the applicable
dividend rate for the period.

Under the Investment Company Act of 1940, the fund is required to maintain
asset coverage of at least 200% with respect to the remarketed preferred
shares as of the last business day of each month in which any such shares are
outstanding. Additionally, the fund is required to meet more stringent asset
coverage requirements under terms of the remarketed preferred shares and the
shares' rating agencies. Should these requirements not be met, or should
dividends accrued on the remarketed preferred shares not be paid, the fund may
be restricted in its ability to declare dividends to common shareholders or
may be required to redeem certain of the remarketed preferred shares. At
October 31, 1997, no such restrictions have been placed on the fund.

Federal tax information
(Unaudited)

The fund has designated 100% of dividends paid from net investment income
during the fiscal year as tax exempt for Federal income tax purposes.

The Form 1099 you receive in January 1998 will show the tax status of all
distributions paid to your account in calendar 1997.



Results of October 9, 1997 shareholder meeting
(Unaudited)

A meeting of shareholders of the fund was held on October 9, 1997.  At the
meeting, each of the nominees for Trustees was elected, as follows:

                               Common Shares           Preferred Shares
                                            Votes                  Votes
                            Votes for    withheld     Votes for  withheld
Jameson Adkins Baxter       3,799,475      61,243        109         0
Hans H. Estin               3,800,262      60,456        109         0
R.J. Jackson                3,799,485      61,233        109         0
Elizabeth T. Kennan         3,799,975      60,743        109         0
Lawrence J. Lasser          3,800,485      60,233        109         0
Donald S. Perkins           3,793,728      66,990        109         0
William F. Pounds           3,799,262      61,456        109         0
George Putnam               3,799,912      60,806        109         0
George Putnam, III          3,795,785      64,933        109         0
A.J.C. Smith                3,800,262      60,456        109         0
W. Nicholas Thorndike       3,799,228      61,490        109         0

A proposal to ratify the selection of Coopers & Lybrand L.L.P. as auditors for
the fund was approved as follows:

Common Shares - 3,797,141 votes for, and 17,310 votes against, with 46,267
abstentions and non-broker votes.

Preferred Shares - 109 votes for, and 0 votes against, with 0 abstentions and
non-broker votes.

All tabulations are rounded to nearest whole number.



Fund information

INVESTMENT MANAGER

Putnam Investment 
Management, Inc.
One Post Office Square
Boston, MA 02109

MARKETING SERVICES

Putnam Mutual Funds Corp. 
One Post Office Square
Boston, MA 02109

CUSTODIAN
Putnam Fiduciary Trust Company

LEGAL COUNSEL
Ropes & Gray

INDEPENDENT ACCOUNTANTS
Coopers & Lybrand L.L.P.

TRUSTEES
George Putnam, Chairman
William F. Pounds, Vice Chairman
Jameson Adkins Baxter
Hans H. Estin
John A. Hill
Ronald J. Jackson
Elizabeth T. Kennan
Lawrence J. Lasser
Robert E. Patterson
Donald S. Perkins
George Putnam, III
A.J.C. Smith
W. Thomas Stephens
W. Nicholas Thorndike

OFFICERS
George Putnam
President 

Charles E. Porter
Executive Vice President 

Patricia C. Flaherty
Senior Vice President 

John D. Hughes
Senior Vice President and Treasurer

Lawrence J. Lasser
Vice President 

Gordon H. Silver
Vice President 

Gary N. Coburn
Vice President 

William J. Curtin
Vice President 

Jerome J. Jacobs
Vice President 

Richard P. Wyke
Vice President and Fund Manager 

William N. Shiebler
Vice President 

John R. Verani
Vice President 

Paul M. O'Neil
Vice President 

Beverly Marcus
Clerk and Assistant Treasurer 



Call 1-800-225-1581 weekdays from 9 a.m. to 5 p.m. Eastern Time for up-to-date
information about the fund's NAV.



[LOGO OMITTED]

PUTNAM INVESTMENTS

The Putnam Funds
One Post Office Square
Boston, Massachusetts 02109

- --------------------
Bulk Rate
U.S. Postage
PAID
Putnam
Investments
- --------------------

36866-215   12/97



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