Answer to Question #309971 in Financial Math for A.Av

Question

Assume the total cost of a tertiary education will be R75 000 when your child

enters university in 18 years. You presently have R7 000 to invest. What rate of

interest must you earn on your investment to cover the cost of your child’s tertiary

education?

Answer 1

Solution

Amount Invested = R 7000

Total Cost of Tertiary Education = R75,000

Time Period = 18 years

Compound Interest Formula

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

Here

$A$ – Final amount which in this case is $R 75,000$

$P$ – Initial amount invested which in this case is $R 7,000$

$r$ – Annual interest rate (required to find)

$n$ – Compounding period per year, which in this case is $1$

$t$ – The number of time periods

 

Using the values, we get

$75000 = 7000{\left( {1 + \frac{r}{1}} \right)^{\left( 1 \right)\left( {18} \right)}}$

${\left( {1 + r} \right)^{18}} = \frac{{75000}}{{7000}}\\$

$r = {\left( {\frac{{75000}}{{7000}}} \right)^{\left( {1/18} \right)}} - 1\\$

$r = 0.1408280192$

Hence the annual interest rate must be 14.08 %