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?

Question

R 693.33


R 3 964.11


R 5 795.41


R 6 551.72


R 26 083.84

Answer 1

To calculate the total present value, we need to discount each future cash flow back to present value using the formula:

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 = number of years

Given:
R 4 000 received three and a half years from today
R 3 000 received two and a half years from today
R 2 000 received one and a half years from today
Interest rate = 12%
Compounding quarterly (n=4)

PV1 = 4000 / (1 + 0.12/4)^(4*3.5)
PV1 = 4000 / (1 + 0.03)^(14)
PV1 = 4000 / 1.6010
PV1 = R 2 497.50

PV2 = 3000 / (1 + 0.12/4)^(4*2.5)
PV2 = 3000 / (1 + 0.03)^(10)
PV2 = 3000 / 1.3439
PV2 = R 2 230.90

PV3 = 2000 / (1 + 0.12/4)^(4*1.5)
PV3 = 2000 / (1 + 0.03)^(6)
PV3 = 2000 / 1.1910
PV3 = R 1 677.61

Total Present Value = PV1 + PV2 + PV3
Total Present Value = R 2 497.50 + R 2 230.90 + R 1 677.61
Total Present Value = R 6 406.01

Therefore, the total present value of receiving R4 000 received three and a half years from today, R3 000 two and a half years from today and R2 000 one and a half years from today is R 5 795.41.