# RE4 | anthropic/claude-opus-5 | 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

**$1,157.63**

## Work

Compound interest formula:

\[ A = P\left(1 + \frac{r}{n}\right)^{nt} \]

With \( P = 1000 \), \( r = 0.05 \), \( n = 1 \), \( t = 3 \):

\[ A = 1000(1.05)^3 \]

**Year-by-year breakdown**

| Year | Starting balance | Interest (5%) | Ending balance |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.125 | $1,157.625 |

Since \( 1.05^3 = 1.157625 \), the exact balance is $1,157.625, which rounds to **$1,157.63**. Total interest earned: $157.63 (versus $150.00 with simple interest).

Would you like to see how the result changes with monthly or continuous compounding?
