A debt of R8 000 is to be discharged by a series of equal quarterly payments over 5 years, the first being made immediately. If the interest rate is 16% p.a. compounded quarterly, find the value of the quarterly payments.

Answer 1

To find the value of the quarterly payments, we can use the formula for the present value of an ordinary annuity:

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

Where:
PV = Present Value of the debt (R8 000)
PMT = Quarterly payment
r = Quarterly interest rate (16% / 4 = 4% or 0.04)
n = Total number of payments (5 years * 4 payments per year = 20 payments)

Plugging in the values, we get:

R8 000 = PMT * [1 - (1 + 0.04)^-20] / 0.04

R8 000 = PMT * [1 - (1.04)^-20] / 0.04

R8 000 = PMT * [1 - 0.4564] / 0.04

R8 000 = PMT * 11.59

PMT = R8 000 / 11.59

PMT ≈ R689.99

Therefore, the value of the quarterly payments should be approximately R689.99.