Question

If a borrower can afford to repay a home loan by making 300 monthly payments of R986.33, how much can be borrowed at 18% per annum compounded monthly?

Answer 1

To calculate how much can be borrowed, we first need to calculate the present value of 300 monthly payments of R986.33 at an interest rate of 18% per annum compounded monthly.

The formula to calculate the present value of a series of equal payments is:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:
PV = present value
PMT = monthly payment amount (R986.33)
r = monthly interest rate (18%/12 = 1.5% or 0.015)
n = number of payments (300)

PV = 986.33 * [(1 - (1 + 0.015)^-300) / 0.015]
PV = 986.33 * [(1 - 0.24029) / 0.015]
PV = 986.33 * (0.75971 / 0.015)
PV = 986.33 * 50.6473
PV = R49,980.26

Therefore, the maximum amount that can be borrowed at 18% per annum compounded monthly is R49,980.26.