Answer to Question #249547 in Financial Math for Nana

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 half-yearly payments for the loan

Answer 1

Let the cost of the home be 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 (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