Question

Philip opened a savings account and deposited $600.00 as principal. The account earns 7% interest, compounded quarterly. What is the balance after 7 years?
Round your answer to the nearest cent.

Answer 1

To calculate the balance of a savings account with compound interest, we can use the formula:

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

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.

Given:
- \( P = 600 \) (the initial deposit)
- \( r = 0.07 \) (7% annual interest rate)
- \( n = 4 \) (compounded quarterly)
- \( t = 7 \) years

Now we plug the values into the formula:

\[
A = 600 \left(1 + \frac{0.07}{4}\right)^{4 \times 7}
\]

Calculate \(\frac{0.07}{4}\):

\[
\frac{0.07}{4} = 0.0175
\]

Now calculate \(A\):

\[
A = 600 \left(1 + 0.0175\right)^{28}
\]
\[
A = 600 \left(1.0175\right)^{28}
\]

Now calculate \( (1.0175)^{28} \):

\[
(1.0175)^{28} \approx 1.650658
\]

Now complete the calculation for \(A\):

\[
A \approx 600 \times 1.650658 \approx 990.395
\]

Finally, round to the nearest cent:

\[
A \approx 990.40
\]

So, the balance after 7 years is **$990.40**.