Solution :
The present value is given by :
[tex]$PV = \frac{FV}{(1+r)^n}$[/tex]
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 :
[tex]$PV = \frac{FV}{(1+r)^n}$[/tex]
[tex]$ = \frac{53,000}{(1+0.0841)^5}$[/tex]
[tex]$=\frac{53000}{1.4974}$[/tex]
= $ 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
[tex]$FV=PV \times (1+r)^n$[/tex]
Particulars Amount
Present value $ 38,206.04
Future value $ 61,400
Periods 8
Therefore, the future value is :
[tex]$FV=PV \times (1+r)^n$[/tex]
[tex]$61,400=38,206.04 \times (1+r)^8$[/tex]
[tex]$(1+r)^8 = \frac{61400}{38206.04}$[/tex]
[tex]$(1+r)^8 = 1.6071$[/tex]
(1 + r) = 1.061096
r = 1.061096 - 1
r = 0.061096
r = 6.1096 %
Therefore, the interest rate per annum is 6.1096%
