Filed Pursuant to Rule 424(b)(3)
Registration Statement No. 333-122977
Registration Statement No. 333-122977
Pricing Supplement to the Prospectus Supplement No. 485 dated March 15, 2005 — No. 510
 | The Goldman Sachs Group, Inc. Medium-Term Notes, Series B 6.60% Mandatory Exchangeable Notes due May 2006 (Exchangeable for Common Stock of Lexmark International, Inc.) |
This pricing supplement and the accompanying prospectus supplement no. 485, relating to the mandatory exchangeable notes, should be read together. Because the mandatory exchangeable notes are part of a series of our debt securities called Medium-Term Notes, Series B, this pricing supplement and the accompanying prospectus supplement no. 485 should also be read with the accompanying prospectus dated March 15, 2005, as supplemented by the accompanying prospectus supplement dated March 15, 2005. Terms used here have the meanings given them in the accompanying prospectus supplement no. 485, unless the context requires otherwise.
The mandatory exchangeable notes offered by this pricing supplement, which we call the “offered notes” or the “notes”, have the terms described in the accompanying prospectus supplement no. 485, as supplemented or modified by the following:
Issuer:The Goldman Sachs Group, Inc.
Face amount:each offered note will have a face amount equal to $63.60, which is the initial index stock price; the aggregate face amount for all the offered notes is $15,582,000
Initial index stock price:$63.60 per share
Original issue price:100% of the face amount
Net proceeds to the issuer:99.95% of the face amount
Trade date:July 27, 2005
Settlement date (original issue date):August 3, 2005
Stated maturity date:May 3, 2006, unless extended for up to six business days
Interest rate (coupon):6.60% per year
Interest payment dates:on the third calendar day of each month, until maturity, commencing on September 3, 2005
Regular record dates:for the interest payment dates specified above, five business days before each interest payment date
Index stock and index stock issuer: common stock of Lexmark International, Inc.
CUSIP no.:38143Y533
Your investment in the notes involves certain risks. We encourage you to read “Additional Risk Factors Specific to Your Note” beginning on page S-3 of the accompanying prospectus supplement no. 485 so that you may better understand those risks. The offered notes are not principal-protected and you could lose your entire investment. In addition, the payment amount is capped.
Neither the Securities and Exchange Commission nor any other regulatory body has approved or disapproved of these securities or passed upon the accuracy or adequacy of this pricing supplement. Any representation to the contrary is a criminal offense.
Goldman Sachs may use this pricing supplement in the initial sale of the offered notes. In addition, Goldman, Sachs & Co. or any other affiliate of Goldman Sachs may use this pricing supplement in a market-making transaction in an offered note after its initial sale.Unless Goldman Sachs or its agent informs the purchaser otherwise in the confirmation of sale, this pricing supplement is being used in a market-making transaction.
Goldman, Sachs & Co.
Pricing Supplement dated July 27, 2005.
Principal amount:
On the stated maturity date, each offered note will be exchanged for index stock at the exchange rate or, at the option of Goldman Sachs, for the cash value of that stock based on the final index stock price.
Exchange rate:
If the final index stock price equals or exceeds the threshold appreciation price, then the exchange rate will equal the threshold fractiontimesone share of index stock for each $63.60 of the outstanding face amount. Otherwise, the exchange rate will equal one share of the index stock for each $63.60 of the outstanding face amount. The exchange rate is subject to anti-dilution adjustment as described in the accompanying prospectus supplement no. 485.
Please note that the amount you receive for each $63.60 of outstanding face amount on the stated maturity date will not exceed the threshold appreciation price and that it could be substantially less than $63.60. You could lose your entire investment in the offered notes.
Final index stock price:
The closing price of one share of the index stock on the determination date, subject to anti-dilution adjustment.
Threshold appreciation price:
The initial index stock pricetimes1.10, which equals $69.96 per share.
Threshold fraction:
The threshold appreciation pricedividedby the final index stock price.
Determination date:
The fifth trading day prior to May 3, 2006, unless extended for up to five business days.
Business day:
As described on page S-17 of the accompanying prospectus supplement no. 485.
Trading day:
As described on page S-17 of the accompanying prospectus supplement no. 485.
No listing :
The offered notes will not be listed on any securities exchange or interdealer market quotation system.
Lexmark International, Inc.:
According to its publicly available documents, Lexmark International, Inc. is a developer, manufacturer and supplier of printing and imaging solutions for offices and homes. Information filed with the SEC by Lexmark International, Inc. under the Exchange Act can be located by referencing its SEC file number: 001-14050.
Historical trading price information:
The index stock is traded on the New York Stock Exchange under the symbol “LXK”. The following table shows the quarterly high and low trading prices and the quarterly closing prices for the index stock on the New York Stock Exchange for the four calendar quarters in each of 2003 and 2004 and the three calendar quarters in 2005, through July 27, 2005. We obtained the trading price information shown below from Bloomberg Financial Services, without independent verification.
S-2
| High | Low | Close | ||||||||||
2003 | ||||||||||||
| Quarter ended March 31 | $67.80 | $57.41 | $66.95 | |||||||||
| Quarter ended June 30 | $76.99 | $67.09 | $70.77 | |||||||||
| Quarter ended September 30 | $77.09 | $59.40 | $63.01 | |||||||||
| Quarter December 31 | $78.64 | $63.31 | $78.64 | |||||||||
2004 | ||||||||||||
| Quarter ended March 31 | $92.00 | $76.32 | $92.00 | |||||||||
| Quarter ended June 30 | $96.53 | $90.20 | $96.53 | |||||||||
| Quarter ended September 30 | $94.97 | $81.50 | $84.01 | |||||||||
| Quarter ended December 31 | $88.93 | $79.57 | $85.00 | |||||||||
2005 | ||||||||||||
| Quarter ended March 31 | $86.10 | $77.90 | $79.97 | |||||||||
| Quarter ended June 30 | $79.92 | $64.83 | $64.83 | |||||||||
| Quarter ending September 30 (through July 27, 2005) | $70.42 | $61.40 | $63.95 | |||||||||
| Closing price on July 27, 2005 | $63.95 | |||||||||||
As indicated above, the market price of the index stock has been highly volatile during recent periods. It is impossible to predict whether the price of the index stock will rise or fall, and you should not view the historical prices of the index stock as an indication of future performance. See “Additional Risk Factors Specific to Your Note¾ The Market Price of Your Note May Be Influenced by Many Unpredictable Factors” in the accompanying prospectus supplement no. 485.
S-3
Hypothetical payment amount:
The table below shows the hypothetical payment amounts that we would deliver on the stated maturity date in exchange for each $63.60 of the outstanding face amount of your note, if the final index stock price were any of the hypothetical prices shown in the left column. For this purpose, we have assumed that there will be no anti-dilution adjustments to the exchange rate and no market disruption events.
The prices in the left column represent hypothetical closing prices for one share of index stock on the determination date and are expressed as percentages of the initial index stock price, which equals $63.60 per share. The amounts in the right column represent the hypothetical cash value of the index stock to be exchanged, based on the corresponding hypothetical final index stock prices, and are expressed as percentages of the initial index stock price. Thus, a hypothetical payment amount of 100% means that the cash value of the index stock that we would deliver in exchange for each $63.60 of the outstanding face amount of your note on the stated maturity date would equal 100% of the initial index stock price, or $63.60, based on the corresponding hypothetical final index stock price and the assumptions noted above.
| Hypothetical Final Index | Hypothetical Payment | |
| Stock Price as % of | Amounts as % of | |
| Initial Index Stock Price | $63.60 Face Amount | |
| 200% | 110% | |
| 175% | 110% | |
| 150% | 110% | |
| 120% | 110% | |
| 115% | 110% | |
| 110% | 110% | |
| 105% | 105% | |
| 100% | 100% | |
| 75% | 75% | |
| 50% | 50% | |
| 0% | 0% |
The payment amounts shown above are entirely hypothetical; they are based on market prices for the index stock that may not be achieved on the determination date and on assumptions that may prove to be erroneous. The actual market value of your note on the stated maturity date or at any other time, including any time you may wish to sell your note, may bear little relation to the hypothetical payment amounts shown above, and those amounts should not be viewed as an indication of the financial return on an investment in the offered notes or on an investment in the index stock. Please read “Additional Risk Factors Specific to Your Note” and “Hypothetical Payment Amounts on Your Note” in the accompanying prospectus supplement no. 485.
S-4
Payments on your note are economically equivalent to the amounts that would be paid on a combination of other instruments. For example, payments on your note are economically equivalent to the amounts that would be paid on a combination of an interest-bearing bond bought, and an option sold, by the holder (with an implicit option premium paid over time to the holder).The discussion in this paragraph does not modify or affect the terms of the offered notes or the United States income tax treatment of the offered notes as described under “Supplemental Discussion of Federal Income Tax Consequences” in the accompanying prospectus supplement no. 485.
Hedging:
In anticipation of the sale of the offered notes, we and/or our affiliates have entered into hedging transactions involving purchases of the index stock on the trade date. For a description of how our hedging and other trading activities may affect the value of your note, see “Additional Risk Factors Specific to Your Note¾ Our Business Activities May Create Conflicts of Interest Between You and Us” and “Use of Proceeds and Hedging” in the accompanying prospectus supplement no. 485.
S-5