Question

What equal annual amount must be deposited for 10 years in order to provide withdrawals of $200 at the end of the second year and increasing by 25% per year until the end of tenth year? The interest rate is 10% compounded annually.

Answer 1

ANSWER:

Increase in withdrawals by 25%

YEAR	0	1	2	3	4	5	6	7	8	9	10
WITHDRAWAL			200	250	312.5	390.625	488.28125	610.3515625	762.9394531	953.6743164	1192.092896

Now we will find the present value of this cash flow at 10%

pv = cash flow in year 2(p/f,i,n) + cash flow in year 3(p/f,i,n) + cash flow in year 4(p/f,i,n) + cash flow in year 5(p/f,i,n) + cash flow in year 6(p/f,i,n) + cash flow in year 7(p/f,i,n) + cash flow in year 8(p/f,i,n) + cash flow in year 9(p/f,i,n) + cash flow in year 10(p/f,i,n)

pv = 200(p/f,10%,2) + 250(p/f,10%,3) + 312.5(p/f,10%,4) + 390.625(p/f,10%,5) + 488.28(p/f,10%,6) + 610.35(p/f,10%,7) + 762.93(p/f,10%,8) + 953.67(p/f,10%,9) + 1,192.09(p/f,10%,10)

pv = 200 * 0.8264 + 250 * 0.7513 + 312.5 * 0.683 + 390.625 * 0.6209 + 488.28 * 0.5645 + 610.35 * 0.5132 + 762.93 * 0.4665 + 953.67 * 0.4241 + 1,192.09 * 0.3855

pv = 165.29 + 187.83 + 213.44 + 242.55 + 275.62 + 313.21 + 355.92 + 404.45 + 459.6

pv = 2,617.91

now we will find the annual equivalent amount.

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

aw = 2,617.91(a/p,10%,10)

aw = 2,617.91 * 0.1627

aw = 426.05

so the annual equal amount that needs to be deposited is $426.05