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Multiple Choice
A perpetuity has a present value (PV) of \$10,000. If the interest rate is 5\%, what is the annual payment (C) of the perpetuity?
A
\$2,000
B
\$10,500
C
\$500
D
\$5,000
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Verified step by step guidance
1
Understand the concept of a perpetuity: A perpetuity is a type of annuity that provides payments indefinitely. The formula to calculate the present value (PV) of a perpetuity is PV = C / r, where C is the annual payment and r is the interest rate.
Rearrange the formula to solve for the annual payment (C): C = PV × r. This step involves isolating the variable C in the formula.
Substitute the given values into the formula: The present value (PV) is \$10,000, and the interest rate (r) is 5% or 0.05. Replace these values in the formula C = PV × r.
Perform the multiplication: Multiply the present value (PV) of \$10,000 by the interest rate (r) of 0.05 to calculate the annual payment (C).
Interpret the result: The calculated annual payment (C) represents the amount that will be paid indefinitely under the perpetuity given the specified interest rate.