Answer to Question #319878 in Financial Math for Sipura

Question

Mabel borrowed an amount of money from her father. The loan will be paid back by means of payments of R25 000 each every second month for six years. An interest rate of 7,5% per year, compounded every two months, will be applicable. The amount of the loan is

Answer 1

The present value, PV, of the loan is

$PV=Pmt[\frac{1-(1+\frac{r}{m})^{-(nm)}}{\frac{r}{m}}]$

Where Pmt is R25000,

n= 6,

m= 6,

r= 0.075(7.5%)

$\therefore R25000[\frac{1-(1+\frac{0.075}{6})^{-(6×6)}}{\frac{0.075}{6}}]$

$PV=R721181.68$

The amount of money Mabel borrowed is $R721181.68$