You invest $2000 at 5% interest compounded annually. What is it worth after 3 years?

Problem: Find the total value of an investment of
2000 at $5\%$ interest compounded annually after $3$ years.

Steps

1. Compound interest formula
   $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
2. Substitute the given values
   $$A = 2000\left(1 + \frac{0.05}{1}\right)^{1 \times 3}$$
3. Simplify inside the parentheses
   $$A = 2000(1.05)^3$$
4. Evaluate the exponent
   $$A = 2000(1.157625)$$
5. Multiply
   $$A = 2315.25$$