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?

Question

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:

\[ \boxed{24682.41} \]