# RE4 | z-ai/glm-5.2 | 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**. This is calculated using the compound interest formula \( A = P(1 + r)^n \), where \( P = 1000 \), \( r = 0.05 \), and \( n = 3 \).

## Calculation

Use the standard compound interest formula:

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

Where:
- \( A \) = final amount
- \( P \) = principal ($1,000)
- \( r \) = annual interest rate (5% = 0.05)
- \( n \) = number of years (3)

Plug in the values:

\[ A = 1000(1 + 0.05)^3 \]

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

\[ A = 1000(1.157625) \]

\[ A = 1157.625 \]

Round to the nearest cent:

\[ A = \$1,157.63 \]

## Year-by-Year Breakdown

| Year | Starting Balance | Interest Earned | 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 |

The total interest earned over 3 years is **$157.63**.

What would the balance be if the interest were compounded monthly instead of annually?
