Question

$____________5. Your brother knows you are taking CMP325 and are fast becoming a financial genius. He plans to retire when he is 55 years old; today is his 18th birthday. If he plans to accumulate $1,000,000 for retirement, how much must he deposit each year in order to reach his goal if his investment will pay 8% interest per year compounded annually?

Answer 1

The question belongs to Annuity Due.

The formula for Annuity Due:

Future Value of Annuity = Annuity *[ { (1+ rate ) ⁿ - 1 } / rate ] * ( 1 + r )

Given:
Rate: 8%
n= 37 years ( 55 years - 18 years)
Future Value of Annuity = $ 1,000,000

Now,

1,000,000 = Annuity * [ { ( 1+0.08 ) ³⁷ - 1 } / 0.08 ] * ( 1+ 0.08 )
1,000,000 = Annuity * [ { ( 1.08 ) ³⁷ - 1 } / 0.08 ] * 1.08
1,000,000 = Annuity * [ { 17.24 - 1 } /1.08 ] * 1.08
1,000,000 = Annuity * [ 16.24 / 1.08 ] * 1.08
1,000,000 = Annuity * [ 203 ] * 1.08
1,000,000 = Annuity * 219.24
Annuity = 1,000,000 / 219.24
Annutiy = $ 4561.21

So, he must deposit $ 4561.21 each year in order to reach his goal.