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Unformatted text preview: kind of arrangement can a bank offer to him?? Reverse Mortgage The bank can offer a reverse mortgage. The bank will appraise the “value” of his property. Based on the appraised “value” of the property, the bank will offer him a lifetime income stream until death. Upon his death, the bank will receive the property and sell it at whatever market price. Example 1 − 1.04 −5 100000 = X + X 0.04 A retiree aged x owns a property which is valued at $10,000 by Nopay bank for a reverse mortgage. The maximum longevity of this retiree is 6 years. Nopay will pay her an income stream for life with the first payment to be received immediately. Mortgage interest rate = 4% per year Determine the annuity income for each year. Discussion: Let X be the annuity income. Setting $100,000 = X + X(11.045)/0.04 X = $18,342.5 What is wrong with this calculation? What other information does the bank need?? Example Contd Nopay needs mortality table for the retiree of age x.
Age (x+) no. of lives Prob of survival to age x+ 0 1000 1 1 900 0.9 2 800 0.8 3 700 0.7 4 0.5 5 0.3 6 0 0 500 300 Let Y be the annual income to the retiree. Possible income stream in terms of Present Value is:
Age (x+) PV of future income Prob of survival to age x+ 0
Y 1
Y/1.04 2
Y/1.042 3
Y/1.043 4
Y/1.044 5
Y/1.045 6
$0 Death 1 0.9 0.8 0.7 0.5 0.3 0 Value of Property = Actuarial Present Value of Income Stream $100,000 = 3.9013Y Y = $25,632 How does this result compare with the one earlier?? Example Let Y be the annual income to the retiree. Possible income stream in terms of Present Value is:
Age (x+) PV of future income 0
Y 1
Y/1.04 2
Y/1.042 3
Y/1.043 4
Y/1.044 5 6 Y/1.045 Y/1.046 Prob of survival to age x+ Expected Value of Each Annual Income 1 Y 0.9
0.9* Y/1.04 0.8
0.8* Y/1.042 0.7
0.7* Y/1.043 0.5
0.5* Y/1.044 0.3 0 0.3* 0* Y/1.045 Y/1.046 End Financing Real Estate...
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 Spring '09
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 Interest, Interest Rate

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