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.

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