Final answer:
The couple receiving monthly checks from a lender has a reverse mortgage, which allows them to convert home equity into cash payments without the need for monthly repayment.
Step-by-step explanation:
A reverse mortgage is a home loan that you do not have to pay back for as long as you live in your home. It can be paid to you in one lump sum, as a regular monthly income, or at the times and in the amounts you want. The loan and interest are repaid only when you sell your home, permanently move away, or die. The couple who purchased a home for cash over 25 years ago and are now receiving monthly checks from a lender to supplement their retirement income are most likely to have a reverse mortgage.
A reverse mortgage allows homeowners, typically seniors, to access the equity in their home and convert it into cash payments, hence, the monthly checks they are receiving. This contrasts with a home equity loan which is a lump sum loan against the home's equity, requiring regular monthly payments, and an adjustable-rate mortgage which usually involves monthly payments made to pay down the mortgage.