To calculate the ending balance for Avery's certificate of deposit (CD) with daily compounding interest, you can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
Given:
- \( P = 8000 \)
- \( r = 3.2% = 0.032 \)
- \( n = 365 \) (since the interest is compounded daily)
- \( t = 1 \) year
Let's plug in these values into the formula:
\[ A = 8000 \left(1 + \frac{0.032}{365}\right)^{365 \times 1} \]
Calculating the values step-by-step:
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Calculate \( \frac{0.032}{365} \): \[ \frac{0.032}{365} \approx 0.000087671232877 \]
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Calculate \( 1 + 0.000087671232877 \): \[ 1 + 0.000087671232877 \approx 1.000087671232877 \]
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Raise the result to the power of \( 365 \): \[ \left(1.000087671232877\right)^{365} \approx 1.03265434008665 \]
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Finally, multiply by the principal: \[ A \approx 8000 \times 1.03265434008665 \approx 8261.23 \]
The closest answer among the choices provided is $8,260.13.