Question

Eliana puts $5,619.00 into an account to use for school expenses. The account earns 4.04% interest, compounded quarterly. How much will be in the account after 10 years?
Use the formula A=P(1+r/n)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

Answer 1

To calculate the final amount \( A \) in the account after 10 years, we will use the formula:

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

where:
- \( P = 5619.00 \) (the principal amount)
- \( r = 0.0404 \) (the interest rate expressed as a decimal)
- \( n = 4 \) (the number of times the interest is compounded per year)
- \( t = 10 \) (the time in years)

Now, we will substitute the values into the formula:

1. Calculate \( \frac{r}{n} \):
\[
\frac{r}{n} = \frac{0.0404}{4} = 0.0101
\]

2. Calculate \( nt \):
\[
nt = 4 \times 10 = 40
\]

3. Now substitute these values into the formula:
\[
A = 5619.00 \left(1 + 0.0101\right)^{40}
\]
\[
A = 5619.00 \left(1.0101\right)^{40}
\]

4. Calculate \( (1.0101)^{40} \):
\[
(1.0101)^{40} \approx 1.488864
\]

5. Finally, calculate \( A \):
\[
A \approx 5619.00 \times 1.488864 \approx 8365.57
\]

Thus, the amount in the account after 10 years will be approximately **$8,365.57**.

Rounding to the nearest cent, the final answer is:
\[
\boxed{8365.57}
\]