Question

Herman invests $6,400
at 5.5
% interest for 7
years compounded quarterly. Find the amount of money in the account after 7
years.

Answer 1

To calculate the amount of money in an account after 7 years with compounded interest, you can use the formula for compound interest:

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

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 for.

Given:
- \( P = 6400 \)
- \( r = 5.5\% = 0.055 \)
- \( n = 4 \) (because the interest is compounded quarterly)
- \( t = 7 \)

Plugging in the values:

\[
A = 6400 \left(1 + \frac{0.055}{4}\right)^{4 \times 7}
\]
\[
A = 6400 \left(1 + \frac{0.055}{4}\right)^{28}
\]
\[
A = 6400 \left(1 + 0.01375\right)^{28}
\]
\[
A = 6400 \left(1.01375\right)^{28}
\]

Now, calculate \( \left(1.01375\right)^{28} \):

\[
1.01375^{28} \approx 1.433579
\]

Now substitute it back into the formula:

\[
A = 6400 \times 1.433579 \approx 9176.50
\]

Thus, the amount of money in the account after 7 years is approximately **$9,176.50**.