Multiple Choice
What is the present value of \$1,000 to be received in 12 years, assuming an annual interest rate of 8\% compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If you earn an annual interest rate of 6.9\% compounded annually, approximately how many years will it take to double your savings?
A
About 7.2 years
B
About 10.4 years
C
About 20.1 years
D
About 14.5 years
Verified step by step guidance1
Step 1: Understand the concept of compound interest and the Rule of 72. The Rule of 72 is a shortcut to estimate the number of years required to double an investment at a fixed annual interest rate. The formula is: \( \text{Years to double} = \frac{72}{\text{Annual Interest Rate}} \).
Step 2: Convert the annual interest rate from a percentage to a decimal for calculation purposes. For example, 6.9% becomes \( 0.069 \).
Step 3: Apply the Rule of 72 formula. Divide 72 by the annual interest rate in decimal form: \( \text{Years to double} = \frac{72}{0.069} \).
Step 4: Perform the division to calculate the approximate number of years it will take to double your savings. This step involves basic arithmetic.
Step 5: Compare the calculated result to the provided options (About 7.2 years, About 10.4 years, About 20.1 years, About 14.5 years) to determine the closest match.
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