A single $100,000 payment is received at the end of year 5. Using annual compounding at a 10% discount rate, what is its present value, rounded to the nearest dollar?
Correct Answer
B) $62,092
100000÷(1+0.1)^5 = 62092.13. Common errors: discounting with simple instead of compound interest gives $66,667; subtracting 10% per year from the payment gives $50,000; compounding forward instead of discounting gives $161,051.
Why This Is the Correct Answer
Option B is correct because PV = $100,000 ÷ 1.10^5 = $100,000 ÷ 1.61051 = $62,092.13, or $62,092. Each year's discount compounds on the prior year's.
Why the Other Options Are Wrong
Option A: $50,000
Option A, $50,000, subtracts 10% of the payment per year: $100,000 × (1 − 0.10 × 5) = $50,000. Present value divides by 1.10^5, giving $62,092.
Option C: $66,667
Option C, $66,667, uses simple interest: $100,000 ÷ (1 + 0.10 × 5) = $66,667. With annual compounding the divisor is 1.10^5 = 1.61051, giving $62,092.
Option D: $161,051
Option D, $161,051, compounds forward: $100,000 × 1.10^5 = $161,051. That is a future value; the present value is $100,000 ÷ 1.10^5 = $62,092.
Future to present: divide
To bring money back to today, divide by (1 + i) to the n; to send it forward, multiply.
How to use: Use it to confirm a present value is smaller than the future payment.
Exam Tip
At a positive discount rate, the present value must be below the future amount, which eliminates any answer above $100,000.
Common Mistakes to Avoid
- -Using simple interest in the divisor
- -Subtracting the rate times years from the payment
- -Computing future value instead of present value
Concept Deep Dive
Analysis
This question tests discounting a single future payment with annual compounding. The present value equals the payment divided by (1 + rate) raised to the number of years. Distractors use simple interest, straight-line subtraction or compounding forward.
Background Knowledge
The present value of $1 factor is 1 ÷ (1 + i)^n. It converts a future amount into its equivalent today at a given discount rate and number of compounding periods.
Real-World Application
An appraiser values the land reversion under a ground lease expiring in five years by discounting the projected land value at a market-supported rate. The present value forms part of the leased-fee valuation.
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