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

Answer:

He must invest R297 521 today.

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

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

$A(t) = P(1 + \frac{r}{n})^{nt}$

$350000= P(1 + \frac{0.0815}{12})^{2*12}$

$P = \frac{350000}{(1 + \frac{0.0815}{12})^{2*12}}$

$P = 297521$

He must invest R297 521 today.