Answer :
To answer the question about the annual effective rate and whether it is the annually compounded rate that produces the same future value after one year as a given nominal rate, let's break it down step by step.
1. Understanding the Terms:
- Nominal Rate: This is the interest rate as stated, without taking into account the effect of compounding. It is usually quoted on an annual basis.
- Effective Annual Rate (EAR): This is the interest rate that is compounded annually and produces the same amount of interest as the nominal rate when interest is compounded more frequently.
2. Definition of Annual Effective Rate:
- The Annual Effective Rate (AER) or Effective Annual Rate (EAR) is the interest rate on an investment or loan restated from the nominal rate and compounded annually.
3. Future Value:
- The future value is the value of an investment at a specific date in the future that is equivalent to the present value with a specified rate of return.
4. How Effective Annual Rate Matches with Nominal Rate:
- The Effective Annual Rate is designed to account for compounding within the year. When interest is compounded annually, the effective annual rate will match with the annual nominal rate.
- For example, if the nominal rate is 5% per year compounded annually, the future value after one year would be the same as if we use the effective annual rate of 5%.
5. Conclusion:
- Therefore, the statement that the annual effective rate is the annually compounded rate that produces the same future value after one year as a given nominal rate is indeed true.
Thus, the answer to the question is:
True
1. Understanding the Terms:
- Nominal Rate: This is the interest rate as stated, without taking into account the effect of compounding. It is usually quoted on an annual basis.
- Effective Annual Rate (EAR): This is the interest rate that is compounded annually and produces the same amount of interest as the nominal rate when interest is compounded more frequently.
2. Definition of Annual Effective Rate:
- The Annual Effective Rate (AER) or Effective Annual Rate (EAR) is the interest rate on an investment or loan restated from the nominal rate and compounded annually.
3. Future Value:
- The future value is the value of an investment at a specific date in the future that is equivalent to the present value with a specified rate of return.
4. How Effective Annual Rate Matches with Nominal Rate:
- The Effective Annual Rate is designed to account for compounding within the year. When interest is compounded annually, the effective annual rate will match with the annual nominal rate.
- For example, if the nominal rate is 5% per year compounded annually, the future value after one year would be the same as if we use the effective annual rate of 5%.
5. Conclusion:
- Therefore, the statement that the annual effective rate is the annually compounded rate that produces the same future value after one year as a given nominal rate is indeed true.
Thus, the answer to the question is:
True
