What is the total present value of receiving R4 000 received three and a half years from today, R 3 000 two and a half years from today and R 2 000 one and a half years from today? An interest rate of 12% p.a. compounded quarterly is used?

Answer 1

To calculate the total present value of the cash flow, we need to discount each amount back to the present using the formula for compound interest:

PV = FV / (1 + r/n)^(nt)

where:
PV = Present Value
FV = Future Value
r = annual interest rate
n = number of compounding periods per year
t = time in years

For the first cash flow of R 4,000 received three and a half years from today:
PV1 = 4000 / (1 + 0.12/4)^(4 * 3.5)
PV1 = 4000 / (1 + 0.03)^14
PV1 = 4000 / (1.03)^14
PV1 = 4000 / 1.53038
PV1 = R 2,614.80

For the second cash flow of R 3,000 received two and a half years from today:
PV2 = 3000 / (1 + 0.12/4)^(4 * 2.5)
PV2 = 3000 / (1 + 0.03)^10
PV2 = 3000 / (1.03)^10
PV2 = 3000 / 1.34392
PV2 = R 2,231.50

For the third cash flow of R 2,000 received one and a half years from today:
PV3 = 2000 / (1 + 0.12/4)^(4 * 1.5)
PV3 = 2000 / (1 + 0.03)^6
PV3 = 2000 / (1.03)^6
PV3 = 2000 / 1.19102
PV3 = R 1,677.47

Therefore, the total present value of receiving R4,000, R3,000, and R2,000 at the specified times in the future is:
Total PV = PV1 + PV2 + PV3
Total PV = R 2,614.80 + R 2,231.50 + R 1,677.47
Total PV = R 6,523.77

Therefore, the total present value of the cash flows is R 6,523.77.