Answer to Question #230400 in Finance for Henok Gezahaegn

Question

Suppose your retirement benefits during your first year of retirement are 50,000.00 Assume that this amount is just enough to meet your cost of living during the first year. However, your cost of living is expected to increase at an annual rate of 5% due to inflation. Suppose you do not expect to receive any cost of living adjustment in your retirement pension. Then, some of your future cost of living has to come from your savings other than retirement pension. If your saving account earns 7% interest a year, how much should you set aside in order to meet this future increase in cost of living over 25 years and how much should you save each year if you will retire after 10 years?

Answer 1

Given

$A_1=50000\\N=25\\i=0.07\\g=0.05$

therefore

$P=A_1[\frac{1-(1+g)^N(1+I)^{-N}}{i-g}]\\P=50000[\frac{1-(1+0.05)^{25}(1+0.07)^{-25}}{0.07-0.05}]\\=940167.22$

Benefit paid after 25 years

$A=50000\\N=25\\i=0.07$

Present value of retirement benefits

$=50000(P/A,7\%,25)\\=50000(11.654)\\=582700$

Additional saving$=940167.22-582700=357467$