Question

Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an additional $20,000 to that account. You earned 8%, compounded semi-annually, for the first ten years, and 6.5%, compounded annually, for the last five years. Required:

a) What is the effective annual interest rate (EAR) you would get for your investment in the first 10 years?

b) How much money do you have in your account today?

c) If you wish to have $85,000 now, how much should you have invested 15 years ago?

Answer 1

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Answer:

(a)

Formula used to compute effective annual rate is as follows:

b)

Amount for $12500 for 10 years compounded semi annually =$12500 + ( 12500*8.160%*10) = $ 22,700

Amount for $32,500 for 5 Years compounded annually =$32500 + (32500*6.5%*5) = $43,062.50

Money in account today = $ 22,700 + $43,062.50 = $65,762.50

c)

Let the required investment amount be A to receive $85,000 after 15 years. Now, calculate the interest amount for the first 10 years then for next five years. Add the interest amount for 10 years, 5 years and the required investment amount which will be equal to the value $85,000 as shown below: