Question

Jill just turned 30. After consulting a financial planner and laying out her retirement goals she calculates that she will need to have a balance of $500,000 in her retireme account to supplement social security she plans to start collecting when she turns 67. She plans to start saving immediately and to invest her funds in a market index fund that is expected to have an a annual return of 7.5% over 37 years she will ne saving money for retirement. How much money does Jill need to save and invest each month in order to reach the goal of having $500,000 by the time she retires at 67?

A. $211.03

B. $195.10

C. 209.72

D. 227.53

Answer 1

Answer: Option (c) $209.72

Let the Amount deposited each month for 37 years = 'x'

Amount required at the time of retirement = $ 500,000

Period (n) = 37 years

Annual Return on Investment (i) = 7.5%

x * FVAF((7.5/12)%, (37*12)months) = $ 500,000

x * FVAF(0.625%, 444 months) = $ 500,000

x * 2384.11 = $ 500,000

x = $ 500,000/2384.11

Therefore, Monthly Investment (x) = 209.72

Computation of FVAF:

FVAF(i%,n periods) =[((1+i)^n)-1]/i