What is the present value of $100,000 to be received in 5 years, assuming a 10% discount rate?
Correct Answer
D) $62,092
Why this is correct: Present Value (PV) = Future Value / (1 + discount rate)^years. Here, PV = 100000 / (1 + 0.10)^5. Calculate step: 1.10^5 = 1.61051. Then, 100000 / 1.61051 = 62092. Why the other choices are wrong: 75000 is a rough 25% discount, not a precise calculation. 90909 is the PV for one year (100000/1.10). 68301 uses the wrong exponent or rate. Exam tip: The PV formula is fundamental. Remember: PV = FV / (1 + i)^n. Use your calculator's power and division functions carefully.
Why This Is the Correct Answer
Option A ($62,092) is correct because it properly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the values: PV = $100,000 ÷ (1.10)^5 = $100,000 ÷ 1.61051 = $62,092. This calculation accurately discounts the future value back to present terms using the compound discount factor. The result shows that $62,092 invested today at 10% annual return would grow to exactly $100,000 in 5 years.
Why the Other Options Are Wrong
Option A: $75,000
Option A ($75,000) is incorrect as it represents a 25% discount from the future value, which would be appropriate for simple interest calculations but ignores the compounding effect over 5 years at 10%.
Option B: $90,909
Option B ($90,909) is incorrect because it appears to discount for only one year ($100,000 ÷ 1.10 = $90,909), failing to account for the full 5-year time period in the calculation.
Option C: $68,301
Option C ($68,301) is incorrect because it appears to use an improper discount calculation, possibly using simple interest instead of compound interest or applying the wrong number of years in the formula.
DIVIDE and POWER Method
Remember 'DIVIDE and POWER': DIVIDE the future value by (1 + rate) raised to the POWER of years. Think 'Future money loses POWER over time, so DIVIDE it down to present value.'
How to use: When you see a present value question, immediately identify the three components: Future Value (what you're dividing), Rate (what you add to 1), and Years (the power/exponent). Then apply DIVIDE and POWER.
Exam Tip
Always double-check that you're using the correct exponent (number of years) and that your calculator is set to the right number of decimal places - present value calculations are sensitive to rounding errors.
Common Mistakes to Avoid
- -Using simple interest instead of compound interest
- -Forgetting to raise (1 + rate) to the power of years
- -Confusing present value with future value formulas
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 income capitalization approaches, discounted cash flow analysis, and determining the current value of future income streams. The concept reflects the time value of money principle that money available today is worth more than the same amount in the future due to its potential earning capacity. Understanding present value allows appraisers to convert future benefits into today's dollars for accurate property valuation.
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 formula PV = FV ÷ (1 + r)^n requires understanding of compound interest, where 'r' is the discount rate and 'n' is the number of periods.
Real-World Application
Appraisers use present value when valuing income-producing properties to discount future rental income streams back to current value, or when analyzing the present worth of future property improvements or lease payments in DCF analysis.
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