Suppose that you are insured for R 150 000 in the event of an accident. The insurance company, upon accident, tells you that this amount will be paid out in the form of an annuity at the end of each month for the next 3 years. If interest is calculated at 12.5% p.a. compounded monthly then what will the monthly payment be?
To calculate the monthly payment, we need to use the formula for the present value of an annuity:
PV = Pmt * [(1 - (1 + r)^-n) / r]
Where:
PV = Present value of the annuity (R 150 000)
Pmt = Monthly payment
r = Monthly interest rate (12.5% / 12 = 1.0417% or 0.010417)
n = Number of months (3 years * 12 = 36 months)
Substitute the values into the formula:
R 150 000 = Pmt * [(1 - (1 + 0.010417)^-36) / 0.010417]
R 150 000 = Pmt * [(1 - 0.75313) / 0.010417]
R 150 000 = Pmt * [27.9234]
Pmt = R 150 000 / 27.9234
Pmt ≈ R 5 375.93
Therefore, the monthly payment will be approximately R 5 375.93.