
RE 611 / Fin 611 – Real Estate Finance
Reverse Mortgages
Practice Problems Solutions
Dr. Stanley D. Longhofer
1) Your grandmother owns a house worth $155,000 and would like to use some of her
equity while she lives in the house. She is considering a reverse annuity mortgage
(RAM) with a 10-year term, 60 percent maximum loan-to-value (LTV) ratio, and
monthly payments at 7.125 percent interest. She will pay a 2 point origination fee on
this loan; this amount will be added to her principal balance at the origination of the
loan.
a) How large of payments will she receive from her lender?
The key with a RAM, is that the LTV ratio is used to determine the maximum
loan balance that will accrue. This value will be the balance due at the end of
the loan term (FV). FV = 155,000 0.60 = 93,000, P/Y = 12, N = 120,
I = 7.125, PV = 0.02 93,000 = 1,860 PMT = $511.91.
Notice that the points are treated as a cash inflow. This is because the lender is
implicitly giving you $1,860 that you use to pay your closing costs. Just as
with the monthly payment, this amount is added to your outstanding principal
balance that you will have to repay at the end of the loan’s term.
b) What will happen at the end of the loan’s term?
In principle, the property will be sold at the end of the loan term in order to pay
off the outstanding principal balance. Many RAMs, however, allow the
borrower to keep the property until they die or sell the home. The monthly
payments on the loan stop, but interest continues to accrue until the loan is
repaid.
c) What will be your grandmother’s effective borrowing cost (EBC) on this
mortgage?
Simply trace the actual cash flows. She will be receiving payments of $511.91
per month for 120 months. At the end of that time she will repay $93,000.
Notice, however, that although two points are paid at the beginning of the
loan, this is not a cash flow item for her; it is simply added to her principal
balance.
P/Y = 12, N = 120, PMT = 511.91, FV = 93,000, PV = 0 I = EBC = 7.87%.
2) Suppose that Jacob owns a house worth $325,000. He would like to tap the equity in
this house to pay general monthly expenses for the next 15 years, at which time he
expects to sell his house.
a) AllStar Mortgage Corporation is willing to offer Jacob a 15-year, 60% LTV RAM
at 8.0% interest with monthly payments. How much will Jacob receive every
month from this mortgage?
N = 180, I = 8.0, PV = 0, FV = 325,000 0.60 = 195,000 PMT = $563.52
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