Question

Twelve years ago, you deposited $25,500 into an investment fund.
Five years ago, you added an additional $15,000 to that account. You earned 9%,
compounded semi-annually, for the first 12 years, and 7.5%, 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 12 years?
b. How much money do you have in your account today?
c. If you wish to have $75 000 now, how much should you have invested 17 years
ago?

Answer 1

ANSWER-

Initial deposit= $25500, Rate= 9% compounded semi annually

Second deposit = $15000, Rate = 7.5% compounded anually

a.

EAR= (1+ periodic rate)^n -1,

where periodic rate = stated annual rate/ n

and n= no. of compounding periods per year

EAR for Initial Deposit=

=9.2025% ANS

b. The amount of money in account today

Principal amount= 25500

effective rate= 9.2025%

year= 12

Current value=

=

=$38157.33

where F = Future value P = Present value r = rate t =years n = Number of compounding periods per year

Principal amount= 38157.33+15000= 53157.33

effective rate= 7.5%

year= 5

Current value=

=

= $76314.22 ANS

c.

Future value= 75000

year= 17

Present value=?

Rate= 9% for 12 years and 7.5% for five years

PV=

=

= $30807.26 ANS