Question

Wallace has an investment opportunity with Bank ABC. Interest is calculated at 8% p.a. compounded annually for the first three years, where after the interest rate will increase by 1% p.a. compounded semi-annually for the remainder of the term. What amount must Wallace invest today to receive R 5 000 in 5 years time?

Answer 1

To calculate the amount Wallace must invest today, we can use the formula for compound interest:

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

where:
A = the future value of the investment (R 5 000)
P = the principal amount (the amount Wallace must invest today)
r = the annual interest rate
n = the number of compounding periods per year
t = the number of years the money is invested for

For the first three years:
A = P(1 + 0.08/1)^(1*3)
A = P(1.08)^3
A = 1.25971P

For the remaining two years:
A = P(1 + 0.09/2)^(2*2)
A = P(1.045)^4
A = 1.21873P

Since the total future value is R 5 000, we can set up the equation:

1.25971P + 1.21873P = 5000
2.47844P = 5000
P = 5000 / 2.47844
P ≈ R 2018.58

Therefore, Wallace must invest approximately R 2018.58 today to receive R 5 000 in 5 years time.