Godfrey is promised to receive R3 000 in two years’ time and R4 500 in three and a half years’ time if he invests his money with Bank A. If the interest rate is 9% p.a. compounded monthly, what amount must he invest today?


R 693.33


R 3 964.11


R 5 795.41


R 6 551.72


R 26 083.84

1 answer

To find the amount Godfrey must invest today, we can work backwards using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money Godfrey will receive in the future
P = the principal amount (the amount he must invest today)
r = the interest rate per period (9% / 12 = 0.75% or 0.0075)
n = the number of compounding periods per year (12)
t = the number of years

First, let's find the future value of R3 000 in two years' time using the formula:

3000 = P(1 + 0.0075/12)^(12*2)
3000 = P(1 + 0.000625)^24
3000 = P(1.015625)^24
3000 = P(1.172160545)
P = 3000 / 1.172160545
P ≈ R2 559.29

Next, let's find the future value of R4 500 in three and a half years' time using the formula:

4500 = P(1 + 0.0075/12)^(12*3.5)
4500 = P(1 + 0.000625)^42
4500 = P(1.015625)^42
4500 = P(1.25241123)
P = 4500 / 1.25241123
P ≈ R3 593.41

Therefore, Godfrey must invest about R2 559.29 for R3 000 in two years' time and R3 593.41 for R4 500 in three and a half years' time, which totals R6 151.70.

Therefore, the correct answer is R 6 551.72.