Question

7. Nkaiseng who is 25 years wants to invest some money for her retirement when she is 65 years. If she invest at a compound interest rate of 11.5% per annum. How much money should she invested if she wants to retire R500 300? Round up your answer to the nearest rand (10 Points).​

Answer 1

The formula for calculating the future value of a present amount with compound interest is:

FV = PV * (1 + r)^n

where FV is the future value, PV is the present value, r is the annual interest rate (as a decimal), and n is the number of compounding periods.

In this case, Nkaiseng wants to invest some money now to retire with R500 300 in 40 years (from 25 to 65). The annual interest rate is 11.5%, which is equivalent to a monthly interest rate of 0.115/12 = 0.00958.

So we have:

FV = PV * (1 + 0.00958)^ (40*12)

500300 = PV * (1.00958)^480

Dividing both sides by (1.00958)^480, we get:

PV = 500300 / (1.00958)^480

PV = 500300 / 20.4524

PV = 24406.53

Therefore, Nkaiseng should invest R24406.53 (rounded up to the nearest rand) now to have R500 300 when she retires at 65 years with an interest rate of 11.5% per annum.