You purchase a new flat for R 250 000, and pay R 50 000 as a down payment. You take out a loan for the remainder at an interest rate of 12% p.a., compounded monthly, for 30 years. Calculate your monthly loan payment.
To calculate the monthly loan payment, we can use the formula for a fixed-rate mortgage loan:
\[ M = \frac{P \cdot r(1+r)^n}{(1+r)^n - 1} \]
where:
M = Monthly loan payment
P = Loan amount (principal) = R 200,000
r = Monthly interest rate = Annual interest rate / 12 = 0.12/12 = 0.01
n = Number of payments = 30 years * 12 months = 360
Substitute the values into the formula:
\[ M = \frac{200000 \cdot 0.01(1+0.01)^{360}}{(1+0.01)^{360} - 1} \]
\[ M = \frac{2000 \cdot (1.01)^{360}}{(1.01)^{360} - 1} \]
\[ M = \frac{2000 \cdot 149.3689}{149.3689 - 1} \]
\[ M = \frac{298,737.8}{148.3689} \]
\[ M = R 2,011.57 \]
Therefore, your monthly loan payment will be R 2,011.57.