Multiple Choice
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
Multiple Choice
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
Verified step by step guidance1
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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