What is the present value of the following cash flow stream at a rate of 6.25\%?\newline\begin{align*}\text{Year 1:} &\quad \$1,000 \\\text{Year 2:} &\quad \$1,500 \\\text{Year 3:} &\quad \$2,000 \end{align*}\text{(Round your answer to the nearest dollar.)}

• A. \$3,970
• B. \$4,200
• C. \$4,150
• D. \$4,060

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the concept of present value (PV). Present value is the current worth of a future cash flow or series of cash flows, discounted at a specific interest rate. The formula for PV 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.
2. Step 2: Break down the cash flow stream into individual components. For this problem, the cash flows are: \( \$1,000 \) in Year 1, \( \$1,500 \) in Year 2, and \( \$2,000 \) in Year 3. Each cash flow will be discounted separately using the formula for present value.
3. Step 3: Apply the present value formula to each cash flow. For Year 1: \( PV_1 = \frac{1,000}{(1 + 0.0625)^1} \). For Year 2: \( PV_2 = \frac{1,500}{(1 + 0.0625)^2} \). For Year 3: \( PV_3 = \frac{2,000}{(1 + 0.0625)^3} \).
4. Step 4: Sum the present values of all cash flows to find the total present value of the cash flow stream. The formula is: \( PV_{total} = PV_1 + PV_2 + PV_3 \).
5. Step 5: Round the total present value to the nearest dollar as instructed in the problem. This will give you the final answer.