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

Solution :

The present value is given by :

$PV = \frac{FV}{(1+r)^n}$

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 :

$PV = \frac{FV}{(1+r)^n}$

      $= \frac{53,000}{(1+0.0841)^5}$

      $=\frac{53000}{1.4974}$

      = $ 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

$FV=PV \times (1+r)^n$

Particulars                  Amount

Present value           $ 38,206.04

Future value             $ 61,400

Periods                        8

Therefore, the future value is :

$FV=PV \times (1+r)^n$

$61,400=38,206.04 \times (1+r)^8$

$(1+r)^8 = \frac{61400}{38206.04}$

$(1+r)^8 = 1.6071$

(1 + r) = 1.061096

r =   1.061096 - 1

r  =   0.061096  

r = 6.1096 %

Therefore, the interest rate per annum is 6.1096%