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? (2 marks) b) How much money do you have in your account today? (4 marks) c) If you wish to have $85,000 now, how much should you have invested 15 years ago?

Answer: a. 8.16%

b. $65,762.5

c. $39,700

Explanation:

Initial investment for 15years = $12500

Investment for 5years = $20000

Interest = 8% compunded semi annually for the first 10 years and 6.5% compunded annually for the last five years.

a. EAR = [1 + (nominal interest rate/the number of compounding periods) ]^number of compounding periods-1

where,

nominal interest = 8 %,

number of compounding periods = 2 (semi annually)

EAR = ([ 1 + (0.08 / 2) ] ^ 2) - 1

= { (1 + 0.04) ^2 } - 1

= { 1.04 } ^ 2 - 1 = 1.0816 - 1

= 0.0816

= 8.16%

b. The amount on $12500 for 10 years compounded semi annually:

= $12500 + (12500*8.160%*10)

= $ 22,700

The amount on $32,500 for 5 Years compounded annually

=$32500 + (32500*6.5%*5)

= $43,062.50

Money in account today:

= $ 22,700 + $43,062.50

= $65,762.5

c. Let the amount be x

For the first 10 years at 8.160 %

Interest Amount = (x * 8.160% * 10)

= 0.8160x

For the next 5 years:

Interest Amount will be,

= (x * 6.5% * 5)

= 0.325x

Total money at end of 15 Years=85000

0.8160x + 0.3250x + x = 85000

2.141x = 85000

x = 85000/2.141

X = $ 39,700 Approx.