Question

# Today is Derek’s 25th birthday. Derek has been advised that he needs to have \$3,491,566.00 in...

Today is Derek’s 25th birthday. Derek has been advised that he needs to have \$3,491,566.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 5.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 30.00th birthday and ending on his 65th birthday. How much must those deposits be?

Solution

Future value of annuity due=Annuity payment*(((1+r)^n-1)/r)*(1+r)

Here Annuity payment= Annual deposits to be made in account

r-intrest rate -5%

n-number of periods=65-30=35

Future value of annuity due=Amount needed on 65th birthday in account= \$3,491,566.

Putting values in formula

3491566=Annuity payment*((((1+.05)^35)-1)/.05)*(1+.05)

Solving we get

Annuity payment=\$36816.76(Annual payments he must make)

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