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\%

Answer: (A)

Verified step by step guidance

1. 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.
2. Identify the given values from the problem: The annual payment \( C \) is \( 85 \) dollars, and the price \( P \) is \( 950 \) dollars.
3. Substitute the given values into the formula: \( r = \frac{85}{950} \). This will give the rate of return as a decimal.
4. 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.
5. 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.