Multiple Choice
What is the future value of \$2,000 deposited for one year at an annual interest rate of 6% compounded once per year?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
All else constant, which one of the following will result in the lowest present value of a lump sum?
A
A lower discount rate
B
A shorter time period until receipt
C
Receiving the lump sum today
D
A higher discount rate
Verified step by step guidance1
Understand the concept of present value: Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return (discount rate). The formula for present value is PV = \( \frac{FV}{(1 + r)^t} \), where FV is the future value, r is the discount rate, and t is the time period.
Analyze the impact of the discount rate: A higher discount rate increases the denominator \((1 + r)^t\), which reduces the present value. Conversely, a lower discount rate decreases the denominator, resulting in a higher present value.
Evaluate the impact of time period: A shorter time period (t) reduces the exponent in \((1 + r)^t\), which increases the present value. A longer time period increases the exponent, reducing the present value.
Consider receiving the lump sum today: If the lump sum is received today, there is no discounting applied (t = 0), and the present value equals the future value. This results in the highest present value.
Conclude that a higher discount rate results in the lowest present value: Among the options provided, a higher discount rate has the most significant impact in reducing the present value of a lump sum.
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