What is the present value of $100,000 to be received in 5 years, assuming a 8% discount rate?
Correct Answer
A) $68,058
Present Value = Future Value ÷ (1 + discount rate)^n = $100,000 ÷ (1.08)^5 = $100,000 ÷ 1.4693 = $68,058.
Why This Is the Correct Answer
Option A ($68,058) is correct because it properly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the given values: PV = $100,000 ÷ (1.08)^5 = $100,000 ÷ 1.4693 = $68,058. This calculation accurately discounts the future value back to present terms using the 8% discount rate over 5 years. The result shows that $68,058 invested today at 8% annual return would grow to exactly $100,000 in 5 years.
Why the Other Options Are Wrong
Option B: $92,593
Option B ($92,593) appears to use an incorrect discount factor, possibly calculating for fewer years or a lower discount rate. This value is too high because it doesn't adequately account for the full 5-year discounting period at 8%. The calculation may have used (1.08)^1 instead of (1.08)^5, or confused present value with a different financial calculation.
Option C: $146,933
Option C ($146,933) represents the future value calculation rather than present value, showing what $100,000 would grow to if invested at 8% for 5 years. This is the reciprocal error - using FV = PV × (1 + r)^n instead of the present value formula. This common mistake occurs when candidates confuse the direction of the time value calculation.
Option D: $108,000
Option D ($108,000) appears to be a simple interest calculation ($100,000 × 1.08) for one year only, ignoring both the compounding effect and the 5-year time period. This demonstrates a fundamental misunderstanding of compound interest and the present value concept, treating it as if only one year of interest applies.
PV-FD Memory Method
Remember 'Present Value = Future Divided' - PV equals the future amount DIVIDED by (1 + rate)^years. Think of it as 'shrinking' the future money back to today's smaller present value. The acronym 'FRED' helps: Future ÷ Rate Exponential = Discounted value.
How to use: When you see a present value question, immediately think 'FRED' and set up the division: Future amount ÷ (1 + discount rate)^number of periods. Always remember you're making the number smaller (discounting), not larger.
Exam Tip
Always double-check whether the question asks for present value or future value - they're opposite calculations. If the answer choices include both a smaller and larger number than the given amount, one is likely PV and the other FV.
Common Mistakes to Avoid
- -Confusing present value with future value formulas
- -Using simple interest instead of compound interest
- -Forgetting to raise the discount factor to the power of the number of periods
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, where future income streams must be converted to current value. 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 compare future cash flows on an equal basis and make informed valuation decisions.
Background Knowledge
Present value is a core financial concept used extensively in real estate appraisal, particularly in the income capitalization approach. Appraisers must understand that money has time value - a dollar today is worth more than a dollar tomorrow due to earning potential and inflation. The discount rate represents the required rate of return or opportunity cost of capital.
Real-World Application
An appraiser valuing an income property needs to determine what a $100,000 lease payment due in 5 years is worth today to properly value the property. Using an 8% discount rate, they calculate the present value as $68,058, which represents the current contribution of that future payment to the property's overall value.
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