Question

Find the periodic payment of a series of payments of Rx each, payable for 3 years in advance every second month if the present value of the payments is R2833. Assume a nominal interest rate of 18% per annum, compounded 6 times per year.

Answer 1

First, calculate the equivalent periodic payment of R2833 using the formula for the present value of an ordinary annuity:

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

where PV is the present value of the payments, R is the periodic payment, r is the periodic interest rate, and n is the total number of periods.

Given that PV = R2833, r = 0.18/6 = 0.03, and n = 3*6 = 18, we can substitute these values into the formula:

2833 = R * [(1-(1 + 0.03)^-18)/0.03]

2833 = R * [(1-0.606477)/0.03]

2833 = R * (0.393523/0.03)

2833 = R * 13.1174

R = 2833 / 13.1174

R ≈ 215.973

Therefore, the periodic payment of the series of payments is approximately R215.97 every second month.