Multiple Choice
If you invest \$5,000 today at an annual interest rate of 6\% compounded annually, how many years will it take for your investment to grow to \$10,000? (Round your answer to the nearest whole year.)
10. Time Value of Money
Time Value of Money Equations
Multiple Choice
The relationship between the present value (PV) and the investment time period, assuming a positive interest rate, is best described as:
A
Present value decreases as the investment time period increases.
B
Present value is not affected by the investment time period.
C
Present value remains constant regardless of the investment time period.
D
Present value increases as the investment time period increases.
Verified step by step guidance1
Understand the concept of Present Value (PV): Present Value is the current worth of a future sum of money or stream of cash flows, given a specified rate of return (interest rate). It is calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the time period.
Analyze the formula: Notice that the denominator (1 + r)^n increases as the time period (n) increases, assuming a positive interest rate (r > 0). This means the present value (PV) will decrease as n increases.
Relate the formula to the problem: Since the denominator grows larger with increasing time periods, the fraction PV = FV / (1 + r)^n becomes smaller, leading to a decrease in PV.
Eliminate incorrect options: Based on the formula, 'Present value remains constant regardless of the investment time period' and 'Present value increases as the investment time period increases' are incorrect because PV is directly affected by the time period and decreases as n increases.
Confirm the correct answer: The correct relationship is 'Present value decreases as the investment time period increases,' which aligns with the mathematical behavior of the formula.
Related Videos
Related Practice
