Answer:
The formula is:
P = (PV * r) / (1 - (1 + r)^(-n))
Where:
P = Size of the periodic payment
PV = Present value (loan amount)
r = Interest rate per compounding period
n = Number of compounding periods
Given information:
PV = Balance financed = Total cost of the home - Down payment
Total cost of the home = R177,175.00 / 0.2 = R885,875.00
Down payment = R177,175.00
r = 9.4% per annum = 0.094 / 2 = 0.047 (semi-annual rate)
n = 20 years * 2 = 40 semi-annual periods
Now, let's calculate the size of the half-yearly payments (P):
PV = R885,875.00 - R177,175.00 = R708,700.00
r = 0.047
n = 40
Using the formula, we have:
P = (708700 * 0.047) / (1 - (1 + 0.047)^(-40))
P ≈ R11,532.42
Therefore, the size of the half-yearly payments for the loan is approximately R11,532.42.
