Banks, brokerage houses, savings and loan associations and mutual funds all report an explosion of interest in Individual Retirement Accounts, as last-minute tax filers suddenly realize what an IRA deduction can do for them.

But time is short and so are many savings accounts. How can you start an IRA if you don't have a handy $2,000 lying around?

Answer: Borrow the money and repay the $2,000 over the next year. The tax cut you get for starting an IRA is greater than the interest you will pay on the loan--and the interest, of course, is itself tax-deductible. Your repayments become a form of forced saving for your own retirement.

What if you have already filed your tax return without an IRA?

Answer: You can borrow the money, start an IRA and file an amended tax return by April 15. This earns you a refund on some of the taxes already paid.

Assuming that you can make the payments, you are better off with a loan and an IRA than you would be by skipping the IRA this year.

And, you are better off if you borrow enough to make the maximum contribution than if you saved something less than the maximum.

IRAs can be started by anyone with earnings who has not yet reached age 70 1/2. An individual can contribute, and tax deduct, up to $2,000 (or $2,250 if he or she has a non-earning spouse); a married working couple can jointly deduct $4,000.

One IRA will save a married couple $440 in 1982 taxes, if their taxable income, after all other deductions and exemptions, is $20,000. Two IRAs will save them $880. On a taxable income of $40,000, one IRA will save them $780 and two IRAs, $1,560.

Without an IRA, that money would go directly to the U.S. Treasury. With an IRA, it all goes into your own savings.

Single people realize even greater savings from an IRA--because they are taxed at higher rates than couples are on the same amount of income. The way the tax system works, the higher your tax rate the more valuable the tax deduction.

On a taxable income of $20,000 a single person will save $613; on a $40,000 income, the savings rise to $880.

A quick way to borrow is against your bank card or by writing a check against your bank credit line. Banks, S&Ls and credit unions will also be amenable to making personal loans for IRAs if you invest the money in the institution's own savings certificates. Yields run from about 8 to 11 percent depending on the institution and on the certificate you choose.

For $2,000, you can get a certificate for 18 months and up. If you're putting away at least $2,500, your range of choices will also include six-month certificates or, at some institutions, a money market deposit account whose interest rate changes anywhere from monthly to daily. The shorter-term deposits will pay the most if interest rates soon rise again and shoot up sharply. Longer-term deposits will pay more if rates decline, stay level or rise only a little bit.

Banking institutions are attracting the lion's share of the IRA money because savings certificates are easy to buy, simple to understand and without risk. Your IRA savings (plus any savings you might have in a Keogh plan for the self-employed) are guaranteed for up to $100,000 at insured banks, S&Ls or credit unions. You get an additional $100,000 worth of coverage for your other accounts at the same institution.

If you're a mutual-fund investor, you may be able to move some money into one of the fund's own IRAs just by making a phone call--so you'll have no trouble making the April 15 deadline. Are you stuck if your fund requires a lengthy exchange of paperwork to establish an IRA? Not at all. The Internal Revenue Service allows you an automatic four-month extension for filing your income-tax return, which lets you make an IRA contribution at any time up to Aug. 15 and still deduct it against your 1982 taxes.

To get the extension, simply file Form 4868 by April 15--but note: The extension is only for filing the tax return. Your total estimated tax must still be paid by April 15.

If you have a brokerage account, you can sell some shares to raise the $2,000 or $4,000 needed for an IRA investment, or you can borrow against those shares. Your stockbroker will arrange for an instant loan and reinvest the proceeds wherever you like--in a money-market mutual fund (whose interest rate changes daily), a mutual fund that buys stocks or bonds, or a self-directed IRA that lets you manage your own investments.

Self-directed IRAs are for people with substantial amounts of money and investment savvy. You need above-average returns to cover the cost of the brokerage commissions and still exceed the best rates now available on bank and S&L certificates.