What is the future value of \$2, invested at an annual interest rate of 5\% compounded annually for 3 years?

• A. \$2.25
• B. \$2.15
• C. \$2.30
• D. \$2.31

Answer: (D)

Verified step by step guidance

1. Understand the formula for future value (FV) when interest is compounded annually: \( FV = PV \times (1 + r)^n \), where PV is the present value, r is the annual interest rate (in decimal form), and n is the number of years.
2. Identify the values given in the problem: Present Value (PV) = \$2, annual interest rate (r) = 5\% or 0.05, and the number of years (n) = 3.
3. Substitute the values into the formula: \( FV = 2 \times (1 + 0.05)^3 \).
4. Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \), then raise it to the power of 3: \( 1.05^3 \).
5. Multiply the result of \( 1.05^3 \) by the present value (PV = \$2) to calculate the future value (FV).