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

The interest is $6128.3

Explanation:

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

`\begin{gathered} FV=P\cdot(1+(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+(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}`