Current Attempt in Progress Which of the following statements is true? O The higher the discount rate, the higher the present value. O The process of accumulating interest on interest is referred to as discounting. O If money is worth 10% compounded annually, $ 2420 due one year from today is equivalent to $ 2200 today. O If a single sum is due on December 31, 2020, the present value of that sum decreases as the date draws closer to December 31,2020.
Current Attempt in Progress Which of the following statements is true? O The higher the discount rate, the higher the present value. O The process of accumulating interest on interest is referred to as discounting. O If money is worth 10% compounded annually, $ 2420 due one year from today is equivalent to $ 2200 today. O If a single sum is due on December 31, 2020, the present value of that sum decreases as the date draws closer to December 31,2020.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Title: Understanding Present Value and Discount Rates**
**Question:**
Which of the following statements is true?
1. The higher the discount rate, the higher the present value.
2. The process of accumulating interest on interest is referred to as discounting.
3. If money is worth 10% compounded annually, $2420 due one year from today is equivalent to $2200 today.
4. If a single sum is due on December 31, 2020, the present value of that sum decreases as the date draws closer to December 31, 2020.
**Options and Concepts Explained:**
1. **Discount Rate and Present Value:**
- Present value is inversely related to the discount rate. As the discount rate increases, the present value decreases. This is because a higher discount rate reduces the present worth of future cash flows.
2. **Discounting vs. Compounding:**
- Discounting is the process of determining the present value of a future amount. Compounding, on the other hand, is the accumulation of interest on an initial sum and on previously accumulated interest.
3. **Interest Rate and Equivalence:**
- This statement involves calculating the present value of a future sum based on a 10% annual interest rate. To verify, use the formula:
\[
\text{Present Value} = \frac{\text{Future Value}}{(1 + r)^n}
\]
- Here, \( r = 0.10 \) and \( n = 1 \).
4. **Time Value of Money:**
- Generally, the present value decreases as the due date approaches, because there is less time to earn interest on the money.
This question tests your understanding of the relationship between discount rates, present value, and key financial concepts like compounding and discounting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0506d55b-bb84-43f9-9218-6fc41e3ed9b6%2Fa397b70a-cd18-4f57-ad37-5c31eeb03f03%2F0a7z9jk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Present Value and Discount Rates**
**Question:**
Which of the following statements is true?
1. The higher the discount rate, the higher the present value.
2. The process of accumulating interest on interest is referred to as discounting.
3. If money is worth 10% compounded annually, $2420 due one year from today is equivalent to $2200 today.
4. If a single sum is due on December 31, 2020, the present value of that sum decreases as the date draws closer to December 31, 2020.
**Options and Concepts Explained:**
1. **Discount Rate and Present Value:**
- Present value is inversely related to the discount rate. As the discount rate increases, the present value decreases. This is because a higher discount rate reduces the present worth of future cash flows.
2. **Discounting vs. Compounding:**
- Discounting is the process of determining the present value of a future amount. Compounding, on the other hand, is the accumulation of interest on an initial sum and on previously accumulated interest.
3. **Interest Rate and Equivalence:**
- This statement involves calculating the present value of a future sum based on a 10% annual interest rate. To verify, use the formula:
\[
\text{Present Value} = \frac{\text{Future Value}}{(1 + r)^n}
\]
- Here, \( r = 0.10 \) and \( n = 1 \).
4. **Time Value of Money:**
- Generally, the present value decreases as the due date approaches, because there is less time to earn interest on the money.
This question tests your understanding of the relationship between discount rates, present value, and key financial concepts like compounding and discounting.
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