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

a.Effective annual interest rate ( EAR) for first 10 years is calculated as follows,

EAR = (1+(i/n))ⁿ -1

where,

i means interest rate

n means no. of compounding periods

EAR = (1+(i/n))ⁿ -1

EAR = (1+(.08/2))² -1

EAR = 8.16%

b. Money in account today is calculated as follows,

If interest is compounded Annually,

FV = PV (1+r)ⁿ

where,

FV means Future Value

PV means Present Value

r means interest rate

n means no. of years

If interest is compounded Semi annually,

FV = PV (1+(r/2))^(nx2)

FV after first 10 years will be,

FV = PV (1+(r/2))^(nx2)

FV = 12,500(1+(.08/2))^(10x2)

FV = $27,389.04

FV after next 5 years will be,

FV = PV (1+r)ⁿ

FV = (27,389.04+20,000)(1+.065)⁵

FV = $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 follows,

FV = PV (1+(r/2))^(nx2) (1+r)ⁿ

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

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

PV = $ 28,314.19