Roughly one-third of people who get Social Security must pay income taxes on their benefits.

Dear Liz,

I will be 66 next month and will start collecting $2,351 a month in Social Security. I plan on working at least another two years. I owe about $55,000 on a second mortgage at 6.875 percent. I have only $6,000 in an IRA. I can join the 401(k) at work, which matches up to 3 percent of contributions. By using all my Social Security, I can pay off the second mortgage in two years. If I choose that, I won’t have any extra money to invest in the 401(k). Should I use Social Security to pay off my second mortgage? Or am I better off investing in the 401(k)?

— Gary

Dear Gary,

Paying off your debt by the time you retire is generally a good idea. However, it’s not so good an idea that you should pass up free money.

Here’s a way to think about it: Paying off your second mortgage would result in a return that’s, at most, equal to the interest rate, or 6.875 percent. If you can deduct the interest payments, your return would be even lower. If you’re in the 25 percent federal tax bracket and can deduct all your interest, the effective rate on your loan would be a little over 5 percent.

Putting the same money into your 401(k), on the other hand, wins you an instant risk-free return equal to the matching rate, which is typically 50 to 100 percent of a portion of your salary.

Your 401(k) offers another benefit: Your contributions lower your tax bill, while paying off your mortgage won’t. That’s important, because at least a portion of your Social Security payments are likely to be taxable.

The tax rate is determined by what’s known as your “combined income.” Combined income is your adjusted gross income and any nontaxable interest plus half of your Social Security benefit.

If you’re single and your combined income is between $25,000 and $34,000, you may owe income tax on up to 50 percent of your Social Security benefits. If your combined income exceeds $34,000, up to 85 percent of your benefits may be taxable. For married couples filing jointly, up to 50 percent of Social Security is taxable when income is between $32,000 and $44,000, while income over $44,000 may trigger taxes on up to 85 percent of Social Security benefits.

This doesn’t mean 50 to 85 percent of your benefit will be taken away — just that it will be subject to income taxes at the usual rates (currently 10 to 39.6 percent).

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