# RE4 | meta/muse-spark-1.1 | run 1

## Prompt

You deposit $1,000 at 5% interest compounded annually. What is the balance after 3 years? Round to the nearest cent and show your work.

## Response

With $1,000 at 5% compounded annually, the balance after 3 years is $1,157.63. This comes from applying the compound interest formula \( A = P(1 + r)^t \) for 3 periods.

## Formula
\[ A = P(1 + r)^t \]
where \( P = 1000 \), \( r = 0.05 \), \( t = 3 \).

## Work
**Year-by-year:**
* Year 1: \( 1000 \times 1.05 = 1050.00 \)
* Year 2: \( 1050.00 \times 1.05 = 1102.50 \)
* Year 3: \( 1102.50 \times 1.05 = 1157.625 \)

**Direct calculation:**
\[ A = 1000 \times (1.05)^3 \]
\[ A = 1000 \times 1.157625 \]
\[ A = 1157.625 \approx 1157.63 \]

Final balance: **$1,157.63**

Want me to show what it would be after 5 or 10 years at the same rate?
