객관식
If a bank charges a customer 15\% annual interest on a loan of \$10,000 compounded annually, what is the total interest earned by the bank after 3 years?
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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\%? Year 1: \$1,000 Year 2: \$1,200 Year 3: \$1,500 \( PV = ? \)
A
\$3,145.48
B
\$3,700
C
\$3,200.00
D
\$3,250.00
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. 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.
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 \$1,200, and for Year 3, it is \$1,500. Each cash flow will be discounted separately using the formula \( PV = \frac{FV}{(1 + r)^n} \).
Step 3: Apply the formula to calculate the PV for Year 1. Substitute \( FV = 1000 \), \( r = 0.08 \), and \( n = 1 \) into the formula: \( PV_{Year1} = \frac{1000}{(1 + 0.08)^1} \).
Step 4: Apply the formula to calculate the PV for Year 2. Substitute \( FV = 1200 \), \( r = 0.08 \), and \( n = 2 \) into the formula: \( PV_{Year2} = \frac{1200}{(1 + 0.08)^2} \).
Step 5: Apply the formula to calculate the PV for Year 3. Substitute \( FV = 1500 \), \( r = 0.08 \), and \( n = 3 \) into the formula: \( PV_{Year3} = \frac{1500}{(1 + 0.08)^3} \). Add the PVs of all three years together to find the total present value: \( PV_{Total} = PV_{Year1} + PV_{Year2} + PV_{Year3} \).
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