Question

The UFS estimates that they will need R 450 000 in one and a half years’ time and another R 720 000 in two and a half years’ time to cover the expected cost of providing each registered student with a Kovsie dairy. If interest is calculated at 6.4% p.a., compounded semi-annually, how much must the UFS invest today in order to cover the expected future costs?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the present value of the future costs, we can use the formula for compound interest:

PV = FV / (1 + r/n)^(n*t)

Where:
PV = Present Value
FV = Future Value (R 450 000 for one and a half years and R 720 000 for two and a half years)
r = interest rate per period (6.4%)
n = number of compounding periods per year (2 for semi-annual compounding)
t = number of years

For R 450 000 in one and a half years:
PV1 = 450,000 / (1 + 0.064/2)^(2*1.5)
PV1 = 447,634.73

For R 720 000 in two and a half years:
PV2 = 720,000 / (1 + 0.064/2)^(2*2.5)
PV2 = 672,298.06

Therefore, the UFS must invest R 447,634.73 today to cover the expected future costs.