Question

An investor has $100 to invest and she invests in short-term, one year discount bonds over the next 3 years. The forecast for one-year interest rates over the next 3 years is 4.5%, 7.5% and 10.5%. What is the future value of her investment, three years from today?

Group of answer choices

$124.13

$133.35

$137.50

$139.55

Answer 1

$124.13

Explaination :

We will be using the compound interest formula to calculate amount at the end of each year.

A = P*(1+r/100)ⁿ where, A= Amount, P= Principal value, r= rate of interest per annum and n= number of years.

Amount at the end of 1st year :

P= $100

r=4.5%

n=1 year.

A= 100*(1+4.5/100)¹ = 100*(1+0.045) = 100*1.045 = $104.5

Amount at the end of first year : $104.5 , now this will act as the principal for second year.

Therefore,

Principal for second year : $104.5

r=7.5%

n= 1year

A= 104.5*(1+7.5/100)¹ = 104.5*(1+0.075) = 104.5*1.075= $112.3375

Amount at the end of second year = $112.3375 which acts as principal for third year.

Thus,

Principal for third year = $112.3375

r=10.5%

n=1 year.

A= 112.3375*(1+10.5/100)¹ = 112.3375*(1+0.105)= 112.3375*1.105=$124.13(Answer)

Therefore, future value of her investment, three years from today will be $124.13.