Multiple Choice
Noah paid off a loan with a simple interest rate of 9.7\% for 4 months. What was the annual percentage rate (APR) for the loan?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the present value of the following cash-flow stream if the interest rate is 6\% per year? \[\begin{align*}\text{Year 1:} & \quad \$1,000 \\\text{Year 2:} & \quad \$1,000 \\\text{Year 3:} & \quad \$1,000 \end{align*}\](A) \$2,673.01(B) \$2,833.39(C) \$2,545.95(D) \$3,000.00
A
\$3,000.00
B
\$2,833.39
C
\$2,545.95
D
\$2,673.01
Verified step by step guidance1
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 interest rate, and \( n \) is the number of periods.
Step 2: Break down the cash-flow stream into individual components. In this problem, there are three cash flows: \( \$1,000 \) in Year 1, \( \$1,000 \) in Year 2, and \( \$1,000 \) in Year 3. Each cash flow will be discounted separately to its present value.
Step 3: Apply the present value formula to each cash flow. For Year 1, the formula is \( PV_1 = \frac{1000}{(1 + 0.06)^1} \). For Year 2, the formula is \( PV_2 = \frac{1000}{(1 + 0.06)^2} \). For Year 3, the formula is \( PV_3 = \frac{1000}{(1 + 0.06)^3} \).
Step 4: Sum the present values of all three cash flows to find the total present value. The total present value is \( PV_{total} = PV_1 + PV_2 + PV_3 \).
Step 5: Verify the calculation by ensuring that the discounting process accounts for the time value of money, and compare the calculated total present value to the given options to identify the correct answer.
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