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Multiple Choice
What is the present value of \$6,811 to be received in one year if the discount rate is 6.5\%? (Round your answer to the nearest dollar.)
A
$6,398
B
$6,811
C
$6,100
D
$7,254
Verified step by step guidance
1
Understand the concept of present value: Present value (PV) is the current worth of a future sum of money given a specific discount rate. It accounts for the time value of money, which states that money today is worth more than the same amount in the future due to its earning potential.
Identify the formula for present value: The formula is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate (expressed as a decimal), and n is the number of periods.
Substitute the given values into the formula: FV = $6,811, r = 6.5% (or 0.065 as a decimal), and n = 1 year. The formula becomes PV = 6811 / (1 + 0.065)^1.
Simplify the denominator: Calculate (1 + 0.065), which equals 1.065. Then raise it to the power of 1 (since n = 1), which remains 1.065.
Divide the future value by the calculated denominator: Divide $6,811 by 1.065 to find the present value. Round the result to the nearest dollar to match the problem's requirements.