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 \( A \):
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Calculate \( \frac{r}{n} \): \[ \frac{r}{n} = \frac{0.12}{4} = 0.03 \]
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Calculate \( nt \): \[ nt = 4 \times 8 = 32 \]
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Now substitute into the formula: \[ A = 9599 \left(1 + 0.03\right)^{32} \]
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Calculate \( 1 + 0.03 \): \[ 1 + 0.03 = 1.03 \]
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Now raise \( 1.03 \) to the power of 32: \[ 1.03^{32} \approx 2.57508 \]
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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:
\[ \boxed{24682.41} \]