Question

Emma deposits $1200 into an account that pays 3% interest, compounded monthly. What is her ending balance after one year?
Screen Sh
2024-0...48.0
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2024-0...48.40
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2024-0...40.01 /
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2024-0...40.30 Al
$1,236.50
$1,709.91

Answer 1

To calculate Emma's ending balance after depositing $1200 into an account with a 3% annual interest rate compounded monthly, we 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 amount of money).
- \( r \) 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 for.

For Emma's account:
- \( P = 1200 \)
- \( r = 0.03 \) (3%)
- \( n = 12 \) (compounded monthly)
- \( t = 1 \)

Plugging in the values:

\[
A = 1200 \left(1 + \frac{0.03}{12}\right)^{12 \times 1}
\]

Calculating step-by-step:

1. Calculate \( \frac{0.03}{12} \):
\[
\frac{0.03}{12} = 0.0025
\]

2. Add 1 to the interest rate:
\[
1 + 0.0025 = 1.0025
\]

3. Calculate \( 12 \times 1 \):
\[
12 \times 1 = 12
\]

4. Raise \( 1.0025 \) to the power of 12:
\[
(1.0025)^{12} \approx 1.0304
\]

5. Multiply by the principal amount:
\[
A \approx 1200 \times 1.0304 \approx 1236.48
\]

Thus, Emma's ending balance after one year is approximately **$1,236.48**. From your options, the closest is **$1,236.50**.