Question

Kuley owns two investments, A and B, that have a combined total value of $73.600. Investment A is expected to pay $53,000 in 5 years from today and has an expected return of 8.41 percent per year. Investment B is expected to pay $61,400 in 8 years from today and has an expected return of R per year. What is R, the expected annual return for investment B

Answer 1

The present value is given by :

`$PV = (FV)/((1+r)^n)$`

Here r = interest rate per period

n = number of periods

Particulars Amount

Future value $ 53,000

Interest rate 8.41%

Periods 5

The present value is :

`$PV = (FV)/((1+r)^n)$`

`$ = (53,000)/((1+0.0841)^5)$`

`$=(53000)/(1.4974)$`

= $ 35,393.96

Therefore, the value of investment A is $ 35,393.96

The value of investment of B = Combined value - value of A

= $ 73600 - $ 35393.96

= $ 38,206.04

The Future Value

`$FV=PV * (1+r)^n$`

Particulars Amount

Present value $ 38,206.04

Future value $ 61,400

Periods 8

Therefore, the future value is :

`$FV=PV * (1+r)^n$`

`$61,400=38,206.04 * (1+r)^8$`

`$(1+r)^8 = (61400)/(38206.04)$`

`$(1+r)^8 = 1.6071$`

(1 + r) = 1.061096

r = 1.061096 - 1

r = 0.061096

r = 6.1096 %

Therefore, the interest rate per annum is 6.1096%