Question

Avery deposits $8000 in a one year CD at 3.2% interest, compounded daily.
What is Avery's ending balance?
$8,258.00
$8,528.72
$8,260.13
$8,000.70

Answer 1

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:

1. Calculate \( \frac{0.032}{365} \):
\[
\frac{0.032}{365} \approx 0.000087671232877
\]

2. Calculate \( 1 + 0.000087671232877 \):
\[
1 + 0.000087671232877 \approx 1.000087671232877
\]

3. Raise the result to the power of \( 365 \):
\[
\left(1.000087671232877\right)^{365} \approx 1.03265434008665
\]

4. 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**.