Question

Shawn puts $9,599.00 into an account to use for school expenses. The account earns 12% interest, compounded quarterly. How much will be in the account after 8 years?
Use the formula A=P1+
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 amount in the account after 8 years with quarterly compounding interest, we will use the formula:

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

Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money, which is $9,599.00).
- \( r \) = annual interest rate (decimal) (12% = 0.12).
- \( n \) = number of times that interest is compounded per year (quarterly means \( n = 4 \)).
- \( t \) = the number of years the money is invested or borrowed (in this case, 8 years).

Now, plugging in the values:

- \( P = 9599 \)
- \( r = 0.12 \)
- \( n = 4 \)
- \( t = 8 \)

Now let's compute \( A \):

1. Calculate \( \frac{r}{n} \):
\[
\frac{r}{n} = \frac{0.12}{4} = 0.03
\]

2. Calculate \( nt \):
\[
nt = 4 \times 8 = 32
\]

3. Now substitute into the formula:
\[
A = 9599 \left(1 + 0.03\right)^{32}
\]
4. Calculate \( 1 + 0.03 \):
\[
1 + 0.03 = 1.03
\]

5. Now raise \( 1.03 \) to the power of 32:
\[
1.03^{32} \approx 2.57508
\]

6. Now multiply by the principal:
\[
A \approx 9599 \times 2.57508 \approx 24682.41
\]

Finally, rounding to the nearest cent, the amount in the account after 8 years will be:

\[
\boxed{24682.41}
\]