Question

A home was bought with a 20% down payment of R177175.00. The balance was financed for 20 years at 9.4% interest per annum, compounded semi-annually. Find the size of the of the half-yearly payment for the Loan

Answer 1

Let the cost of the home= x,

Therefore, 20% of x= R177175

X= R885875, which is the total payment.

Balance= R885875-R177175

= R708700.

Determination of half years installment payment using the formula below;

$P=A[\frac{1-{(1+\frac{r}{m})^{-n}}}{\frac{r}{m}}]$

Where P= balance or future payments= R708700, A= Installment payment half years, r= interest rate per annum= 9.4% or 0.094, n= number of years= 20years and m= compounding periods i.e half yearly=2.

$R708700=A[\frac{1-{(1+\frac{0.094}{2})^{-20}}}{\frac{0.094}{2}}]$

$A= R9203.796587$

The size of the half-yearly payment for the loan is R9203.796587