Question

A loan will be paid back by means of payments of R250 each, every six month for ten years. An interest rate of 5% per year, compounded every six months, will be applicable. The present value of the loan is

Answer 1

The present value, PV is given as:

$Pmt(\frac{1-\frac{1}{\left(1+\frac{r}{m}\right)^{\left(n\times m\right)}}}{\frac{r}{m}})$

Where Pmt is the monthly payment R250

R is the interest rate 5% or 0.05

N is the number of years 10

M is the number of compounding periods 2

$\therefore$

$PV= R250(\frac{1-\frac{1}{\left(1+\frac{0.05}{2}\right)^{\left(2\times10\right)}}}{(\frac{0.05}{2})})$

$PV=R3897.29$