Answer to Question #221928 in Financial Math for Thamka

Question

Mr Mahlangu invests R20 000,00 to pay for lobola. After 48 months he receives R65 000,00. The 

interest on the investment is compounded quarterly. Determine the yearly interest rate at which the 

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

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

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

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

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

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

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

$4.305788578=4+r$

$r=0.31$%