Multiple Choice
Which formula is used to calculate the present value (PV) of a perpetuity given a constant perpetual cash flow (C) and a discount rate (r)?
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10. Time Value of Money
Time Value of Money Equations
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Given a present value of $1,000, an annual interest rate of 6\% compounded annually, and a time period of 3 years, what is the future value (FV) using the time value of money equation?
A
$1,200.00
B
$1,191.02
C
$1,060.00
D
$1,180.00
Verified step by step guidance1
Step 1: Understand the formula for calculating Future Value (FV) using the time value of money equation. The formula is: FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate (expressed as a decimal), and n is the number of years.
Step 2: Convert the annual interest rate from a percentage to a decimal. For a 6% interest rate, divide 6 by 100 to get r = 0.06.
Step 3: Identify the values given in the problem: PV = $1,000, r = 0.06, and n = 3 years.
Step 4: Substitute the values into the formula: FV = 1000 × (1 + 0.06)^3. Use the exponentiation operation to calculate (1 + 0.06)^3.
Step 5: Multiply the result of (1 + 0.06)^3 by the present value (PV = $1,000) to find the future value (FV).
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