Final answer:
To calculate the future value of $2,000 compounded annually for 10 years at 4%, you use the formula Future Value = Principal × (1 + Rate)^n. The future value equates to approximately $2,960.48.
Step-by-step explanation:
The question is asking to calculate the future value of a $2,000 investment compounded annually for 10 years at a 4 percent interest rate. The formula for future value with compound interest is Future Value = Principal × (1 + Rate)^n, where Principal is the initial amount ($2,000), Rate is the annual interest rate (4% or 0.04), and n is the number of years the money is invested (10).
Let's calculate it step by step:
- Convert the interest rate from a percentage to a decimal by dividing by 100: 4% ÷ 100 = 0.04.
- Substitute the values into the formula: $2,000 × (1 + 0.04)^{10}.
- Calculate the result: $2,000 × (1.04)^{10} = $2,000 × 1.48024 ≈ $2,960.48.
The future value of $2,000 compounded annually at a 4 percent interest rate for 10 years is approximately $2,960.48.