Question

Frank needs to pay R60 000,00 towards his son’s university fees in three years’ time. If he has R46 150,30 now, at what interest rate per year compounded monthly, must he invest his money?

Answer 1

Using compound interest, it is found that he must invest his money at a rate of 8.78% a year.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

• 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.

In this problem, the parameters are as follows:

t = 3, A(t) = 60000, P = 46150.3, n = 12.

Hence:

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

$60000 = 46150.3\left(1 + \frac{r}{12}\right)^{12 \times 3}$

$\left(1 + \frac{r}{12}\right)^{36} = 1.3$

$\sqrt[36]{\left(1 + \frac{r}{12}\right)^{36}} = \sqrt[36]{1.3}$

$1 + \frac{r}{12} = (1.3)^{\frac{1}{36}}$

$1 + \frac{r}{12} = 1.00731451758$

$\frac{r}{12} = 0.00731451758$

r = 12 x 0.00731451758

r = 0.0878.

He must invest his money at a rate of 8.78% a year.

More can be learned about compound interest at brainly.com/question/25781328