Multiple Choice
At an annual interest rate of 12.5\%, how many years will it take for an investment to triple in value if interest is compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the annual rate of return (to the nearest percent) earned on a \$1,000 investment that grows to \$1,800 in six years? (Assume interest is compounded annually.)
A
9%
B
10%
C
11%
D
8%
Verified step by step guidance1
Step 1: Understand the formula for calculating the annual rate of return when interest is compounded annually. The formula is: \( FV = PV \times (1 + r)^t \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual rate of return, and \( t \) is the time in years.
Step 2: Substitute the given values into the formula. Here, \( FV = 1800 \), \( PV = 1000 \), and \( t = 6 \). The equation becomes: \( 1800 = 1000 \times (1 + r)^6 \).
Step 3: Isolate \( (1 + r)^6 \) by dividing both sides of the equation by \( 1000 \). This simplifies to: \( (1 + r)^6 = \frac{1800}{1000} \).
Step 4: Simplify \( \frac{1800}{1000} \) to \( 1.8 \). The equation now becomes: \( (1 + r)^6 = 1.8 \).
Step 5: Solve for \( r \) by taking the sixth root (or raising both sides to the power of \( \frac{1}{6} \)) and then subtracting 1. The equation becomes: \( r = (1.8)^{\frac{1}{6}} - 1 \).
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