Answer to Question #190109 in Financial Math for NN HLONGWANE

Question

A home was bought with a 20%down payment of 177175,00. The balance was financed for 20 years at 9.4 %interest per annum, compounded semi-annually. Find the size of the half yearly payment for the loan.

Answer 1

Let's make a proportion and find the full amount of the loan:

20 % - 177175,00

100%-x

$x=\frac{177 175\times100}{20}=885875$

find the balance:

$885 875-177 175=708 700$ The balance

Find the amount of the semi-annual loan payment:

$r=\frac{9.4}{2}=\frac{4.7}{100}=0.047$

$n=20\times2=40$

$A=\frac{S\times r}{1-(1+r)^{-n}}=\frac{708 700\times 0.047}{1-(1+0.047)^{-40}}=39619$