At a 10% annual rate, what is the present value of $1,000 due one year from today?
Correct Answer
C) $909.09
Present value is the amount that, compounded at the given rate, grows to the future amount: $1,000 ÷ 1.10 = $909.09. Subtracting 10% of $1,000 gives $900, and $1,100 is a future value, not a present value.
Why This Is the Correct Answer
Option C is correct because present value is the amount that, compounded at the given rate, grows to the future amount. $1,000 / 1.10 = $909.09, and $909.09 compounded at 10% for one year grows back to $1,000. This is the standard discounting calculation for one period.
Why the Other Options Are Wrong
Option A: $1,100.00
Option A is wrong because $1,100.00 is a future value, produced by compounding forward ($1,000 x 1.10 = $1,100). The question asks for present value, which is $1,000 / 1.10 = $909.09.
Option B: $900.00
Option B is wrong because $900.00 comes from subtracting the rate from the future amount ($1,000 x (1 - 0.10) = $900). Discounting divides by 1.10 rather than subtracting 10%, giving $909.09.
Option D: $1,000.00
Option D is wrong because $1,000.00 ignores the time value of money entirely. Money due in one year is worth less today when a 10% return is available, so its present value is $1,000 / 1.10 = $909.09.
Forward multiply, backward divide
Moving money forward in time, multiply by (1 + rate); moving it back to today, divide by (1 + rate). Present value is a trip backward, so divide.
How to use: Use this direction rule to decide whether to multiply or divide by 1.10 in any one-period value question.
Exam Tip
Check that the present value is less than the future amount when the rate is positive, and remember that dividing by 1.10 is not the same as subtracting 10%.
Common Mistakes to Avoid
- -Subtracting the rate instead of dividing by 1 plus the rate
- -Compounding forward when asked for present value
- -Ignoring the time value of money
Concept Deep Dive
Analysis
This question tests the basic time-value-of-money concept of discounting. A future amount is converted to present value by dividing by (1 + rate) for each period. With one year at 10%, the calculation is a single division by 1.10.
Background Knowledge
Present value reflects the principle that a dollar received in the future is worth less than a dollar today because of the return that could be earned in the meantime. Discounting divides a future amount by (1 + rate) raised to the number of periods. This concept underlies yield capitalization and discounted cash flow analysis in the income approach.
Real-World Application
An appraiser analyzing a lease that pays a lump sum of $1,000 in one year discounts it at a market-supported 10% rate. The present value of about $909.09 is what that future payment contributes to value today.
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