Question

# \$____________5. Your brother knows you are taking CMP325 and are fast becoming a financial genius. He...

\$____________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?

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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