Question

3. What equal annual amount must be deposited for 10 years in order to provide withdrawals of $300 at the end of second year, S600 at the end of third year, $900 at the end of fourth year, and so on, up to the tenth year? The interest rate is 10% compounded annually.

Answer 1

ANSWER:

N = 10 YEARS

I = 10%

Withdrawals from 2nd year = $300

increase in withdrawals per year = $300

pw = withdrawal in 2nd year(p/f,i,n) + withdrawal in 3rd year(p/f,i,n) + withdrawal in 4th year(p/f,i,n) + withdrawal in 5th year(p/f,i,n) + withdrawal in 6th year(p/f,i,n) + withdrawal in 7th year(p/f,i,n) + withdrawal in 8th year(p/f,i,n) + withdrawal in 9th year(p/f,i,n) + withdrawal in 10th year(p/f,i,n)

pw = 300(p/f,10%,2) + 600(p/f,10%,3) + 900(p/f,10%,4) + 1200(p/f,10%,5) + 1500(p/f,10%,6) + 1800(p/f,10%,7) + 2100(p/f,10%,8) + 2400(p/f,10%,9) + 2700(p/f,10%,10)

pw = 300 * 0.8264 + 600 * 0.7513 + 900 * 0.683 + 1200 * 0.6209 + 1500 * 0.5645 + 1800 * 0.5132 + 2100 * 0.4665 + 2400 * 0.4241 + 2700 * 0.3855

pw = 247.92 + 450.78 + 614.7 + 745.08 + 846.75 + 923.76 + 979.65 + 1017.84 + 1040.85

pw = 6867.33

aw = pw(a/p,i,n)

aw = 6867.33(a/p,10%,10)

aw = 6867.33 * 0.1627

aw = 1117.31

so the equal amount to be deposited for 10 years is $1,117.31