A unique approach to aiding the troubled auto, housing and savings industries was announced today by Dry Dock Savings Bank: using the interest on savings accounts to lease American-made cars and investing the remaining deposits in mortgages.

Under the plan, a customer would deposit between $17,500 and $53,500 in Dry Dock for three years. In place of interest, the customer would have the use of a new car, ranging from a Chevrolet Chevette for the smaller deposit to a Cadillac Seville for the larger amount.

After three years, the customer would get the original deposit back. Bank officials claim their leasing fees are 10 percent below those in the open market.

The program is being made available nationwide. Bank Chairman Robert H. Steele said he would consider it successful if 1,000 contracts were signed. At an average of $30,000 per account, that would mean new deposits of $30 million. One-third of that would go to finance the cars and two-thirds would go into mortgages at 16 percent.

Dry Dock also hopes to bolster its bottom line. The eighth-largest savings bank in this city had a fourth-quarter 1981 loss of $21.9 million. Should losses continue at that rate, its current $84.4 million surplus would be exhausted this year.

If the new program is a success, the bank will look at the possibility of leasing yachts and executive jets.

To lease the least expensive models--a Chevette or Pontiac T-1000--the customer deposits $17,500. Monthly interest, earned at the rate of 14.1 percent, amounts to $216. From that, $204.17 is subtracted as a leasing fee. The remainder continues to accrue interest. At the end of three years, total interest amounts to $8,146.15. Lease payments are $7,350.12. So the customer gets back $796.03 in interest plus the $17,500 principal.

Should the customer purchase the same car through Dry Dock, the list price of $7,690 plus sales tax and finance charges would amount to $10,800 over three years, or about $300 a month. When the anticipated trade-in price of $2,450 is subtracted, the net cost of buying would be $8,350 or $1,000 more than Dry Dock's lease price.

On the most expensive model, the $26,000 Seville, the monthly leasing cost would be $624.17 (this price does not include insurance or maintenance). If an $8,000 trade-in value is assumed at the end of three years, the purchaser's net cost would be $26,500; the leaser's cost, $22,470.

Cars are ordered to customer specification. If the customer has to wait two months for delivery, interest accrues in the account, and the three-year lease takes effect upon delivery. In the case of the Seville, a 60-day wait would add about $2,000 more to the customer's return of interest. The amount returned would be $4,469 plus $53,500 principal.

Customers also have an option to purchase the car at the end of the leasing period. The price would be the average of the wholesale and retail prices as determined by the National Automobile Dealers Association.

These calculations do not take taxes into account. Although the 18 percent financing rate is tax deductible, so is the cost of leasing as a business expense for many individuals.