Question

A bursary fund pays R2 000 at the beginning of each semester for a period of 4 years to a Kovsie student. The account from which these payments are made earns interest at 8% p.a. compounded semi-annually. What amount was needed in the account at the beginning of the 4-year period to make these payments possible?

R 13 064.53


R 14 004.11


R 17 061.67


R 7 002.05

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the amount needed in the account at the beginning of the 4-year period, we need to find the present value of the tuition expenses.

The formula for the present value of an annuity is:
PV = A * ((1 - (1 + r)^-n) / r)
where:
PV = Present Value
A = Annuity payment per period
r = interest rate per period
n = number of periods

In this case:
A = R2,000
r = 8%/2 = 4% = 0.04
n = 8 semesters (4 years * 2 semesters per year)

PV = R2,000 * ((1 - (1 + 0.04)^-8) / 0.04)
PV = R2,000 * ((1 - (1.04)^-8) / 0.04)
PV = R2,000 * ((1 - 0.65543078) / 0.04)
PV = R2,000 * (0.34456922 / 0.04)
PV = R2,000 * 8.6142305
PV = R17,228.46

Therefore, the amount needed in the account at the beginning of the 4-year period to make these payments possible is approximately R17,228.46.

So the closest option is:
R 17 061.67