In a fixed-term, level-payment reverse mortgage, sometimes called a reverse annuity mortgage, or RAM, a lender agrees to pay the homeowner a monthly payment, or annuity, and expects to be repaid from the homeowner's equity when he or she sells the home or obtains other financing to pay off the RAM. Consider a household that owns a $150,000 home free and clear of mortgage debt. The RAM lender agrees to a $100,000 RAM for 10 years at 6 percent. Assume payments are made annually, at the beginning of each year to the homeowner. Calculate the annual payment on the RAM.

Question

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The correct answer is A because the annual payment on the RAM is $7,157.35. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, the present value of the annuity is $100,000, the annual interest rate is 6%, and the number of years is 10. Plugging these values into the formula, we get:$100,000 = PMT * [1 - (1 + 0.06)^-10] / 0.06$100,000 = PMT * [1 - 0.55839] / 0.06$100,000 = PMT * 7.15735PMT = $7,157.35

In a Fixed-Term, Level-Payment Reverse Mortgage, Sometimes Called a Reverse