Question
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.
Answers
GPT 3.5
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.
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.