Answer to Question #319876 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 an ordinary annuity is given by the formula,

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

Where PMT is R25000,

N, number if years= 6,

M, periods of compounding= 6 and is

R, rate= 0.075(7.5%)

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

$PV=R721181.68$

The loan is $R721181.68$