Question

Banabas must pay his ex-wife an amount of R350 000 in two years’ time. Calculate the amount that he must invest today to have this amount available, assuming that Bank X offered him an in interest rate of 8.15% per annum compounded monthly.

Answer 1

He must invest R297 521 today.

Explanation:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Banabas must pay his ex-wife an amount of R350 000 in two years’ time.

This means that
`t = 2, A(t) = 350000`

Interest rate of 8.15% per annum compounded monthly:

This means that
`r = 0.0815, n = 12`.

Amount he must invest today:

This is P. So

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

`350000= P(1 + (0.0815)/(12))^(2*12)`

`P = (350000)/((1 + (0.0815)/(12))^(2*12))`

`P = 297521`

He must invest R297 521 today.