Multiple Choice
Inga took out a \$10,000 loan at an annual interest rate of 6%, to be repaid in equal annual installments of \$1,500. After making payments for 4 years, how many more years will it take Inga to fully pay off the loan?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If interest rates rise, what happens to the present value of a future cash flow, assuming all other factors remain constant?
A
The present value remains unchanged.
B
The present value decreases.
C
The present value increases.
D
The present value becomes negative.
Verified step by step guidance1
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 is calculated using the formula: PV = \( \frac{FV}{(1 + r)^n} \), where FV is the future value, r is the interest rate, and n is the number of periods.
Recognize the relationship between interest rates and present value: The interest rate (r) is inversely related to the present value. As the interest rate increases, the denominator \((1 + r)^n\) becomes larger, reducing the present value.
Analyze the scenario: If interest rates rise while all other factors (future cash flow, time period) remain constant, the present value of the future cash flow will decrease because the discounting effect becomes stronger.
Eliminate incorrect options: The present value does not remain unchanged because it is directly affected by the interest rate. It does not increase because higher interest rates reduce the present value. It does not become negative because the formula for present value does not produce negative values under normal circumstances.
Conclude the correct answer: Based on the relationship between interest rates and present value, the correct answer is that the present value decreases when interest rates rise.
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