A policyholder is given the choice to be paid the interest amount of R 15 000 in cash or in the form of an annuity at the end of each month for 8 years. If interest is calculated at 13 % per annum compounded monthly, how much will the monthly payment of the annuity be?
R 3 480
R 3 125.80
R 1 967.27
R 252
To calculate the monthly payment of the annuity, we can use the annuity formula:
PMT = (PV * r) / (1 - (1 + r)^(-n))
Where:
PMT = monthly payment of the annuity
PV = present value of the interest amount (R 15,000)
r = monthly interest rate (13% per annum compounded monthly = 13%/12 = 1.0833%)
n = total number of payments (8 years * 12 = 96 months)
Plugging in the values:
PMT = (15,000 * 0.010833) / (1 - (1 + 0.010833)^(-96))
PMT = 162.495 / (1 - 0.231029)
PMT = 162.495 / 0.768971
PMT = R 211.28
Therefore, the monthly payment of the annuity will be approximately R 211.28.