In a fixed-term, level-payment reverse mortgage, sometimes called a reverse annu

Question

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.

Explanation / Answer

7157.35

FV of annuity due = (1+r)*PMT*((1+r)n - 1) / r

100000 = (1+6%)*PMT*((1+6%)10 - 1) / 6%

PMT = 100000*6% / ((1+6%)*((1+6%)10 - 1))

= 7157.35

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