If \$1,000\( is invested at an annual interest rate of \)5\%\( compounded annually, what will be the value of the investment after \)3$ years?

• A. \$1,050.00$
• B. \$1,200.00$
• C. \$1,150.00$
• D. \$1,157.63$

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the formula for compound interest, which is \( A = P \cdot (1 + r)^t \), where \( A \) is the future value of the investment, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the number of years the investment is held.
2. Step 2: Identify the values given in the problem: \( P = 1000 \), \( r = 0.05 \) (convert \( 5\% \) to decimal), and \( t = 3 \).
3. Step 3: Substitute the values into the formula: \( A = 1000 \cdot (1 + 0.05)^3 \).
4. Step 4: Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \), so the formula becomes \( A = 1000 \cdot (1.05)^3 \).
5. Step 5: Calculate \( (1.05)^3 \) and then multiply the result by \( 1000 \) to find the future value of the investment. This will give the final answer.