객관식
If the interest rate is 6\% per year, what is the present value (PV) of \$1,000 to be received in 3 years? (Assume annual compounding.)
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10. Time Value of Money
Time Value of Money Equations
객관식
What is the present value (PV) of the following set of cash flows, discounted at an annual rate of 8\%? \[ \begin{align*} \text{Year 1:} & \quad \$1,000 \\ \text{Year 2:} & \quad \$1,500 \\ \text{Year 3:} & \quad \$2,000 \end{align*} \] Choose the closest answer.
A
\$4,000
B
\$4,200
C
\$3,870
D
\$4,011
검증된 단계별 안내1
Step 1: Understand the concept of Present Value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return (discount rate). The formula for PV of a single cash flow is: \( PV = \frac{FV}{(1 + r)^n} \), where \( FV \) is the future value, \( r \) is the discount rate, and \( n \) is the number of periods.
Step 2: Break down the problem into individual cash flows for each year. For Year 1, the cash flow is \( \$1,000 \), for Year 2, it is \( \$1,500 \), and for Year 3, it is \( \$2,000 \). Each cash flow will be discounted separately using the formula for PV.
Step 3: Apply the PV formula to each cash flow. For Year 1, calculate \( PV_1 = \frac{1000}{(1 + 0.08)^1} \). For Year 2, calculate \( PV_2 = \frac{1500}{(1 + 0.08)^2} \). For Year 3, calculate \( PV_3 = \frac{2000}{(1 + 0.08)^3} \).
Step 4: Sum up the present values of all individual cash flows to find the total present value. The formula is: \( PV_{total} = PV_1 + PV_2 + PV_3 \).
Step 5: Compare the calculated total present value to the given answer choices and select the closest value. The correct answer is \( \$4,011 \), which is closest to the calculated total PV.
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