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?
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.