# RE4 | meta/muse-spark-1.1 | run 2

## 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

The balance after 3 years is 1,157.63 dollars. This is 1,000 dollars compounded at 5% annually for 3 years, totaling 157.63 dollars in interest.

## Formula
Compound interest formula with annual compounding:

\[ A = P(1 + r)^t \]

where \( P = 1000 \), \( r = 0.05 \), \( t = 3 \).

## Calculation

1.  Substitute values:
\[ A = 1000(1 + 0.05)^3 \]

2.  Simplify inside parentheses:
\[ A = 1000(1.05)^3 \]

3.  Calculate the power:
\[ (1.05)^2 = 1.1025 \]
\[ (1.05)^3 = 1.1025 \times 1.05 = 1.157625 \]

4.  Multiply by principal:
\[ A = 1000 \times 1.157625 = 1157.625 \]

5.  Round to nearest cent:
\[ A = 1157.63 \]

The final balance is **1,157.63 dollars**.

Would you like me to show how the balance grows year-by-year or with a different compounding frequency?
