You do not start saving money until age 46. On your 46th birthday you dutifully

Question

You do not start saving money until age 46. On
your 46th birthday you dutifully invest $10,000 each
year until you finish your deposits when you reach the
age of 65. The annual interest rate is 8% that you earn
on your deposits. Your brother starts saving $10,000 a
year on his 36th birthday but stops making deposits
after 10 years. Hethen withdraws the compoundedsum
when he reaches age 65. How much more money will
your brother have than you at age 65? Choose one of
the following.

a. Your brother will not have more money than you
have
b. $50,000
c. $176,000
d. $217,600

Explanation / Answer

FV of annuity = P { (1+r)^n - 1} / r

When I start investing $10000 on my 46th birthday, the amount after 20 years i.e. at 65 years of age will be:

FV = 10000 * (1+.08)^20 - 1) / .08 = $457619.64

When my brother starts investing $10000 on on his 36th birthday, the amount after 10 years i.e. at 46 years of age will be:

FV = 10000 * (1+.08)^10 - 1) / .08 = $144865.62

This amount shall now rem,ain invested upto his 65 years of age i.e. for further 20 years. FV of this shall be:

FV = PV(1+r)^n

FV = 144865.62 (1+.08)^20 =$675212.47

Thus I will have $457619.64 at 65 years of age and my brother will have $67512.47.

My brother will have $217592.83 ($67512.47 - $457619.64) more i.e. about $217600 more. Option d is correct

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