What is the future value of \$10 invested for 3 years at an annual interest rate of 5\% compounded annually?

• A. \$11.50
• B. \$11.58
• C. \$10.50
• D. \$15.00

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the formula for future value when interest is compounded annually. The formula is FV = PV × (1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate (in decimal form), and n is the number of years.
2. Step 2: Identify the values given in the problem. The present value (PV) is \$10, the annual interest rate (r) is 5% (convert this to decimal form as 0.05), and the number of years (n) is 3.
3. Step 3: Substitute the values into the formula. Using MathML, the formula becomes: $\mathrm{FV}=\mathrm{PV}\times (1+r){(}^{\mathrm{n}}$. Replace PV with 10, r with 0.05, and n with 3.
4. Step 4: Calculate the expression inside the parentheses first: (1 + r). This becomes (1 + 0.05), which equals 1.05.
5. Step 5: Raise the result to the power of n (3 years): 1.05^3. Then multiply this result by the present value (10) to find the future value.