Last July I wrote that interest on a Treasury bill is income for tax purposes in the year in which the bill matures and is redeemed.

Since then I have been getting letters from readers who feel that this is contrary to the general rule that income is reported in the year it is received. The people who wrote--and perhaps many of you who didn't write--look upon the discount check they get immediately after the auction as prepaid interest.

Let's take a look at what is really happening. We'll assume you have $10,000 with which you want to buy a six-month T-bill. Your bank or broker can handle the purchase for you (for a small fee), but since you work in the District convenient to the Bureau of Public Debt, you decide to take care of it personally.

So you walk into the office and leave a non-competitive bid for next Monday's auction, along with a certified check for $10,000.

(A non-competitive bid means that you agree in advance to pay the average price of all the bids accepted by the Treasury Department from the various institutional buyers like banks and pension funds.

(If you prefer, you can submit a competitive bid--one in which you specify the price you are willing to pay. But then you run the risk of not getting the bill at all; the Treasury Department starts with the highest bid and works its way down until it has all the funds it is looking for.)

Let's assume the average bid was $9,250--a discount of 15 percent on an annual basis, or $750 for the six-month bill.

Shortly after the auction, the Treasury Department will send you a ''discount check'' for $750--and this is what generates the confusion. That $750 is not your interest payment.

Instead, it is a refund to you of what is essentially an initial overpayment--the difference between your $10,000 deposit (with the bid) and the actual cost of the T-bill based on the auction.

Since that discount check is not an interest payment, it is not taxable income when it is received. You get the interest income six months later, when the bill matures and the Treasury Department pays you the full face amount of $10,000.

I hope this explanation helps you to understand why the interest is taxable income in the year in which the bill matures rather than in the year in which it is bought.

Now let me go a step further and point out that the yield on a T-bill is something different from the discount rate. That's because you have invested not the $10,000 of the original certified check, but only the net amount after the discount refund.

In our example, a discount of 15 percent means that you have only the net amount of $9,250 invested for the six months. The $750 interest received at maturity figures out to a yield (on an annual non-compounded basis) of 16.2 percent.

Question: My daughter and her husband are buying a home, taking over the present first mortgage and also taking a second mortgage. The total payments are more than they can afford, so we and my son-in-law's parents are assuming the responsibility for the second mortgage. Can we deduct the interest we each pay on our tax returns?

Answer: It depends on what you mean by ''assuming the responsibility'' for the mortgage payments. There are two tests for you to deduct interest payments: You must be legally responsible, and you must actually make the payments.

From your letter it is apparent that you will meet the second test by making the payments yourselves. The sticky part will be the question of legal liability.

You will be okay if you co-sign the loan agreement or otherwise acknowledge to the lender your legal responsibility for the payments. Your obligation must be enforceable in a court of law (in case of default).

But if you simply have a commitment to your children to make the payments, with no formal and legally enforceable commitment to the lender, then the payments are considered gifts to the children, and the interest element is not deductible.

In fact, the interest can't be claimed by anyone--not by you or the other parents, in the absence of a legal obligation; and not by your daughter and son-in-law because they are not making the payments.