Multiple Choice
If $1 is invested today at an annual interest rate of 3.5\% compounded annually, how much will it be worth after 75 years?
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10. Time Value of Money
Time Value of Money Equations
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A perpetuity pays \$85 per year and costs \$950. What is the rate of return?
A
8.95\%
B
9.50\%
C
7.50\%
D
11.20\%
Verified step by step guidance1
Understand the concept of perpetuity: A perpetuity is a type of annuity that provides payments indefinitely. The formula to calculate the rate of return (or yield) for a perpetuity is: \( r = \frac{C}{P} \), where \( C \) is the annual payment and \( P \) is the price of the perpetuity.
Identify the given values from the problem: The annual payment \( C \) is \( 85 \) dollars, and the price \( P \) is \( 950 \) dollars.
Substitute the given values into the formula: \( r = \frac{85}{950} \). This will give the rate of return as a decimal.
Convert the decimal result into a percentage by multiplying by 100: \( r \times 100 \). This step ensures the rate of return is expressed as a percentage.
Compare the calculated percentage rate of return with the provided answer choices (8.95\%, 9.50\%, 7.50\%, 11.20\%) to determine the correct answer.
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