What is the present value of $100,000 to be received in 5 years, assuming a 6% discount rate?
Correct Answer
D) $74,726
Why this is correct: Present Value (PV) discounts a future sum back to today. PV = Future Value / (1 + discount rate)^number of periods. Here, PV = 100000 / (1 + 0.06)^5. Calculate (1.06)^5 = 1.06 * 1.06 * 1.06 * 1.06 * 1.06 = 1.3382255776. Then, 100000 / 1.3382255776 ≈ 74726. Why the other choices are wrong: $94,340 is close to 100000/1.06, ignoring the compounding over 5 years. $133,823 is the future value (100000 * 1.338). $106,000 is 100000 plus one year of interest. Exam tip: For PV, remember money in the future is worth less today. The formula is PV = FV / (1+i)^n.
Why This Is the Correct Answer
Option A ($74,726) is correct because it properly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the values: PV = $100,000 ÷ (1.06)^5 = $100,000 ÷ 1.3382255776 = $74,725.82, which rounds to $74,726. This calculation correctly discounts the future value back to present terms using the compound discount factor.
Why the Other Options Are Wrong
Option A: $94,340
Option A ($94,340) appears to use an incorrect discount rate or time period in the calculation, possibly using simple interest instead of compound interest or a different rate entirely.
Option B: $133,823
Option B ($133,823) represents the future value calculation instead of present value, using the formula FV = PV × (1 + r)^n, which would be $100,000 × (1.06)^5 if $100,000 were the present value.
Option C: $106,000
Option C ($106,000) incorrectly applies simple interest for one year (6% × $100,000 = $6,000 + $100,000 = $106,000) rather than using the compound present value formula for five years.
PV-FD Memory Method
Remember 'Present Value = Future Divided' - PV always involves dividing the future value by (1 + rate)^years. Think 'going backward in time = divide, going forward in time = multiply'.
How to use: When you see a present value question, immediately think 'divide the future amount' and set up: Future Value ÷ (1 + discount rate)^number of years.
Exam Tip
Always double-check whether the question asks for present value or future value - they use opposite formulas (divide vs. multiply), and this is a common source of confusion on exams.
Common Mistakes to Avoid
- -Confusing present value with future value formulas
- -Using simple interest instead of compound interest
- -Forgetting to raise (1 + rate) to the power of years
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value, which is the current worth of a future sum of money given a specific discount rate. Present value calculations are essential in real estate appraisal for determining the current value of future income streams, such as rental income or proceeds from property sales. The concept recognizes that money received in the future is worth less than the same amount received today due to the time value of money and opportunity cost. Understanding present value is crucial for income approach valuations and investment analysis in real estate.
Background Knowledge
Present value is a core financial concept that calculates today's value of money to be received in the future, accounting for the time value of money through a discount rate. The discount rate reflects the opportunity cost of capital and risk associated with the future payment.
Real-World Application
Appraisers use present value when valuing income-producing properties to determine what future rental income streams are worth today, or when analyzing the present worth of a property's projected sale price at the end of a holding period.
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