Multiple Choice
If $1,000 is invested at an annual interest rate of 6\% compounded annually, what will be the value of the investment after 3 years?
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10. Time Value of Money
Time Value of Money Equations
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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
$1,157.63$
Verified step by step guidance1
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.
Step 2: Identify the values given in the problem: \( P = 1000 \), \( r = 0.05 \) (convert \( 5\% \) to decimal), and \( t = 3 \).
Step 3: Substitute the values into the formula: \( A = 1000 \cdot (1 + 0.05)^3 \).
Step 4: Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \), so the formula becomes \( A = 1000 \cdot (1.05)^3 \).
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.
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