Consider a 30 year mortgage where the principle amount is R200 000 and the annual interest rate is compounded monthly at 6%. What will the monthly payment of this mortgage be?
To calculate the monthly payment of a mortgage, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:
M = P[r(1+r)^n]/[(1+r)^n-1]
Where:
M = monthly payment
P = principle amount (R200 000)
r = monthly interest rate (annual interest rate / 12)
n = total number of payments (number of years * 12)
First, we need to calculate the monthly interest rate:
r = 6% / 12 = 0.06 / 12 = 0.005
Next, we need to calculate the total number of payments:
n = 30 years * 12 = 360
Now, we can plug the values into the formula:
M = 200000[0.005(1+0.005)^360]/[(1+0.005)^360-1]
M = 200000[0.005(1.005)^360]/[(1.005)^360-1]
M = 200000[0.005(2.4281676138)]/[2.4281676138-1]
M = 200000[0.0121408381]/1.4281676138
M = 2421.68
Therefore, the monthly payment for this mortgage will be approximately R2421.68.