A bank offers a perpetuity that pays $1,000 per year, with the first payment occurring at Year 1 and identical payments each year thereafter.

The interest rate is 10% APR, compounded annually.

What is the perpetuity’s present value today?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

Question

A bank offers a perpetuity that pays $1,000 per year, with the first payment occurring at Year 1 and identical payments each year thereafter.

The interest rate is 10% APR, compounded annually.

What is the perpetuity’s present value today?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

BlackTom AI · Accepted Answer

Step 1: Identify the cash flow pattern. This is a perpetuity paying a fixed amount of 1,000 every year starting at Year 1 and continuing forever. Step 2: Recall the present value formula for a perpetuity. For a perpetuity with payment PMT and interest rate r (per period), the present value today is PV = PMT / r, provided payments occur at the end of each period and the rate is per period. Step 3: Confirm the rate period alignment. The problem states an APR of 10% compounded annually, which means the effective annual rate is 10% per year, i.e., r = 0.10 per year. Step 4: Apply the formula. Substitute PMT = 1,000 and r = 0.10 into PV = PMT / r, giving PV = 1,000 / 0.10. Step 5: Compute the value. 1,000 divided by 0.10 equals 10,000. Step 6: Consider rounding instruction. Since the result is 10,000.00 exactly, the final rounded value is 10,000.00. Step 7: Final check. The calculation is consistent with perpetuity theory: the present value is the payment amount displaced by the discount rate over an infinite horizon, which yields 10,000 in this case.

COMM_V 298 101 102 103 2025W1 2025W1 COMM 298 Midterm Exam October 17, 2025 - Requires Respondus LockDown Browser

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