# RE4 | perplexity/sonar-pro | 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 will be **\$1,157.63**. This uses the standard compound interest formula with annual compounding at 5%.

## Step-by-step work

We use the **compound interest formula** for annual compounding:  
\[
A = P(1 + r)^t
\]  
where:  
- \(P\) = principal (initial deposit)  
- \(r\) = annual interest rate (decimal)  
- \(t\) = number of years  
- \(A\) = amount after \(t\) years  

This is a special case of the general formula \(A = P(1 + r/n)^{nt}\) with \(n = 1\) (compounded annually).[Compound Interest Formula](https://www.calculatorsoup.com/calculators/financial/compound-interest-calculator.php)[Compound Interest - Wikipedia](https://en.wikipedia.org/wiki/Compound_interest)

Given:  
- \(P = 1000\)  
- \(r = 0.05\) (since 5% = 0.05)  
- \(t = 3\) years  

Plug into the formula:  
\[
A = 1000(1 + 0.05)^3
\]

Compute inside the parentheses:  
\[
1 + 0.05 = 1.05
\]

Now raise to the 3rd power:  
\[
1.05^3 = 1.05 \times 1.05 \times 1.05
\]  
\[
1.05^2 = 1.1025
\]  
\[
1.1025 \times 1.05 = 1.157625
\]

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

Round to the nearest cent:  
\[
A \approx \$1{,}157.63
\]

So, the **balance after 3 years** is **\$1,157.63**.

Would you like to see how the balance grows year-by-year for those 3 years as well?
