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 will 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 money should you invested 15 years ago?

Answer 1

a. Effective annual interest rate (EAR) for first ten years is calculated using the following formula

Effective annual interest rate = (1 + (i/n))ⁿ - 1

where,

i means nominal interest rate

n means no. of compounding periods

Effective annual interest rate = (1 + (i/n))ⁿ - 1

Effective annual interest rate = (1+ (.08/2))² - 1

Effective annual interest rate = 8.16 %

b. Money in account today is calculated using the following formula

Future value = PV (1+r)ⁿ

where,

PV means present value

r means rate of interest

n means no. of years

if interest is compounded semi annually, then following formula is used

Future value = PV(1+(r/2))^(nx2)

Future value after first ten years will be,

Future value = PV(1+(r/2))^(nx2)

Future value = 12500 (1+(.08/2))^(10x2)

Future value = $27,389.04

Future value after next five years will be,

Future value = PV ( 1+r)ⁿ

Future value = (27,389.04+20,000)( 1+.065)⁵

Future value = $64,927.09 i.e. money in account today

c.To get $85,000 now, money to be invested 15 years ago is calculated as,

Future value = PV( 1+(r/2))^(nx2) ( 1+r)ⁿ

85,000 = PV (1+(.08/2))^(10x2) x( 1+.065)⁵

PV = 85000 / (1+(.08/2))^(10x2) x( 1+.065)⁵

PV = $28,314.19