Answer to Question #198898 in Financial Math for Thandolwenkosi Xab

Question

Mr Mahlangu invests R20000 to play lobola. After 48 months he receives 65000. The interest on the investment is compounded quarterly. Determine the yearly interest rate at which money was invested. Give your answer as a percentage rounded to two decimal places.

Answer 1

Given that

PV= R2000

Total period (n)= 48 (or 4 years)

Compounding periods (m)= 4

Rate(r)= ?

FV= R65000

Where FV is given as

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

$\therefore$ $65000=20000(1+\frac{r}{4})^{4×4}$

$\frac{65000}{20000}=(\frac{4+r}{4})^{16}$

$3.25=(\frac{4+r}{4})^{16}$

$3.16^{\frac{1}{16}}=\frac{4+r}{4}$

$1.076447145=\frac{4+r}{4}$

$4.305788578=4+r$

$r=0.31$%