Question

Wayne is saving up money to buy a car. Wayne puts $8,000.00 into an account which earns 1% interest, compounded quarterly. How much will he have in the account after 8 years?
Round your answer to the nearest cent.

Answer 1

To calculate the amount in the account after 8 years with quarterly compounding interest, we can use the formula for compound interest:

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

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

Given:
- \(P = 8000\)
- \(r = 0.01\) (1% expressed as a decimal)
- \(n = 4\) (since the interest is compounded quarterly)
- \(t = 8\)

Now, we can substitute in those values:

\[
A = 8000 \left(1 + \frac{0.01}{4}\right)^{4 \cdot 8}
\]

Calculating \( \frac{0.01}{4} \):

\[
\frac{0.01}{4} = 0.0025
\]

Now, substituting this back into the formula:

\[
A = 8000 \left(1 + 0.0025\right)^{32}
\]
\[
A = 8000 \left(1.0025\right)^{32}
\]

Next, we calculate \( (1.0025)^{32} \):

\[
(1.0025)^{32} \approx 1.08328231851
\]

Now multiply this result by the principal:

\[
A \approx 8000 \cdot 1.08328231851 \approx 8666.25854808
\]

Finally, rounding this to the nearest cent:

\[
A \approx 8666.26
\]

Thus, after 8 years, Wayne will have approximately **$8,666.26** in the account.