객관식
Given the following cash flow stream: \$1,000 at the end of Year 1, \$1,500 at the end of Year 2, and \$2,000 at the end of Year 3, what is the future value at the end of Year 3 if the interest rate is 6.5% compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
How does an increase in the interest rate affect the present value of a future cash flow?
A
The present value first increases and then decreases as the interest rate increases.
B
The present value remains unchanged regardless of the interest rate.
C
The present value increases as the interest rate increases.
D
The present value decreases as the interest rate increases.
검증된 단계별 안내1
Understand the concept of present value: Present value (PV) is the current worth of a future cash flow, discounted at a specific interest rate. It reflects the time value of money, where money today is worth more than the same amount in the future due to earning potential.
Recall the formula for present value: PV = \( \frac{FV}{(1 + r)^n} \), where FV is the future value, r is the interest rate, and n is the number of periods. This formula shows how future cash flows are discounted back to their present value.
Analyze the relationship between interest rate and present value: As the interest rate (r) increases, the denominator \((1 + r)^n\) becomes larger, which reduces the present value (PV). This is because higher interest rates imply a greater discounting effect.
Consider the implications: The present value decreases as the interest rate increases because the future cash flow is discounted more heavily. This aligns with the principle that higher interest rates reduce the value of money received in the future.
Review the options provided: Based on the explanation and formula, the correct answer is 'The present value decreases as the interest rate increases.' This is consistent with the mathematical relationship between interest rate and present value.
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