Yes. The rules for taxing benefits do not change as a person gets older. Whether or not your Social Security payments are taxed is determined by your income level — specifically, what the Internal Revenue Service calls your “provisional income.”
Provisional income is adjusted gross income (line 11 on your 1040 tax form) plus tax-exempt interest income plus 50 percent of your Social Security payments. If those add up to more than $25,000 for an individual or $32,000 or a married couple filing jointly, you pay federal taxes on a portion of your benefits, regardless of your age.
That includes spousal, survivor and disability benefits as well as retirement benefits. Supplemental Security Income — monthly cash assistance for low-income disabled, blind and older people that is administered but not funded by Social Security — is not taxable.
Keep in mind
People who keep working after retirement will continue to pay FICA taxes on their income as well.