Question

To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $220,000 by the end of 42 years from today. You plan to make equal, annual, end-of-year deposits into an account paying 8% annual interest.

a. How large must the annual deposits be to create the $220,000 fund by the end of 42 years?

b. If you can afford to deposit only $600 per year into the account, how much will you have accumulated by the end of the forty-second year?

Answer 1

a)To get the amount of each annual payment (PMT) ;

$PMT={FVA _{42}} ÷(\frac{(1+0.08)^{42}-1} {0.08})$

PMT=$\frac{220,000}{304.244}$

PMT =$723.10

b)To calculate the future value, FVA;

$FVA_{42}=PMT ×(\frac{(1+0.08)^{42}-1} {0.08})$

Future value(FVA₄₂) =$600× (304.244)

FVA=$182,546.40