# RE4 | anthropic/claude-opus-5 | 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

**$1,157.63**

## Work

Compound interest formula:

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

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

\[ A = 1000(1.05)^3 = 1000 \times 1.157625 = 1157.625 \]

Rounded to the nearest cent: **$1,157.63**

## Year-by-Year Breakdown

| Year | Starting Balance | Interest Earned (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 | $55.13 | $1,157.63 |

Total interest earned: **$157.63** — which is $7.63 more than simple interest ($150.00) would yield, due to compounding.

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