Question

principal of $8,270 is placed in an account that earns interest at the rate of 8% and is compounded quarterly.Approximately how much interest is earned on the investment at the end of 7 years? Show your work.

Answer 1

ANSWER:

The interest is $6128.3

STEP-BY-STEP EXPLANATION:

We have the following formula to calculate the interest generated over time:

$\begin{gathered} FV=P\cdot(1+\frac{r}{n})^{n\cdot t} \\ \text{where P is the principal, r is the interest rate, n is the time period and t is the time} \end{gathered}$

Therefore:

The period of time is quarterly, therefore n is equal to 4, since during a year there are 4 quarters. Replacing:

$\begin{gathered} FV=8270\cdot(1+\frac{0.08}{4})^{4\cdot7} \\ FV=14398.3 \end{gathered}$

This would be the total value to be paid, the interest generated would be the subtraction between the initial value (principal) and this total value, therefore:

$\begin{gathered} I=14398.3-8270 \\ I=6128.3 \end{gathered}$