Answer to Question #215080 in Financial Math for Sherri

Question

The Tanners have received an $8000 gift from one of their parents to invest in their child’s college education. They estimate that they will need $20,000 in 12 years to achieve their educational goals for their child. What interest rate compounded semiannually would the Tanners need to achieve this goal?

Answer 1

$A=P\times[1+r]^t$

Where A is the amount earned. P is the principal amount. R is the rate of interest. T is the number of times interest is compounded.

t is the number of times the interest gets compounded. As it is compounded twice a year we will simply multiply the number of years by 2, which will give us 24.

P is $8000 and A is $20000.

r we have to find out.

Now, placing the figures in the formula:

$20000=8000\times[1+r]^{24}\\2.5=[1+r]^{24}\\2.5^{{\frac{1}{24}}}=[1+r]\\1.039=1+r\\r=3.9\%$

As this interest rate is calculated semi-annually we will convert this in annual interest rate. So, we will multiply this rate by2, as the number of times interest is compounded is two.

So, the rate of interest is 7.8%