(Click on the following icon in order to copy its contents into a spreadsheet.) Compounding per Year Effective Period APR Periodic Rate Annual Rate Semiannual Quarterly Monthly Daily 8% 9% 4. 7.5% 12 4.25% 365
(Click on the following icon in order to copy its contents into a spreadsheet.) Compounding per Year Effective Period APR Periodic Rate Annual Rate Semiannual Quarterly Monthly Daily 8% 9% 4. 7.5% 12 4.25% 365
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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Transcribed Image Text:The image contains a table titled "Data Table" related to financial calculations, specifically for determining periodic rates and effective annual rates from given information.
### Table Details:
- **Columns**:
- **Period**: Refers to how often interest is compounded.
- **APR (Annual Percentage Rate)**: The nominal interest rate for a year.
- **Compounding per Year**: The number of times the interest is compounded annually.
- **Periodic Rate**: The interest rate applied in each compounding period (to be calculated).
- **Effective Annual Rate**: The annual interest rate after accounting for the effects of compounding (to be calculated).
- **Rows**:
1. **Semiannual**:
- **APR**: 8%
- **Compounding per Year**: 2
- **Periodic Rate**: ?
- **Effective Annual Rate**: ?
2. **Quarterly**:
- **APR**: 9%
- **Compounding per Year**: 4
- **Periodic Rate**: ?
- **Effective Annual Rate**: ?
3. **Monthly**:
- **APR**: 7.5%
- **Compounding per Year**: 12
- **Periodic Rate**: ?
- **Effective Annual Rate**: ?
4. **Daily**:
- **APR**: 4.25%
- **Compounding per Year**: 365
- **Periodic Rate**: ?
- **Effective Annual Rate**: ?
The table prompts users to calculate the missing "Periodic Rate" and "Effective Annual Rate" values based on APR and compounding frequency. Additionally, there is an instruction to click a specific icon to copy the table contents into a spreadsheet. The table has options for "Print" and "Done" at the bottom.
![### Periodic Interest Rates
In the following table, fill in the periodic rates and the effective annual rates (EARs).
#### Table 1: Periodic Rates Calculation
| Period | APR | Compounding per Year | Periodic Rate | Effective Annual Rate |
|-------------|-------|----------------------|---------------|-----------------------|
| Semiannual | 8% | 2 | | |
| Quarterly | 9% | 4 | | |
| Monthly | 7.5% | 12 | | |
| Daily | 4.25% | 365 | | |
**Instructions:** Fill in the periodic rates in the table above. Round to two decimal places.
#### Table 2: Effective Annual Rates Calculation
| Period | APR | Compounding per Year | Periodic Rate | Effective Annual Rate |
|-------------|-------|----------------------|---------------|-----------------------|
| Semiannual | 8% | 2 | 4.00% | |
| Quarterly | 9% | 4 | 2.25% | |
| Monthly | 7.5% | 12 | 0.63% | |
| Daily | 4.25% | 365 | 0.01% | |
**Instructions:** Fill in the effective annual rates in the table above. Round to two decimal places.
---
### Explanation
1. **APR (Annual Percentage Rate):** The annual rate of interest without accounting for compounding within the year.
2. **Compounding per Year:** The number of times interest is applied to the balance in a year.
3. **Periodic Rate:** The interest rate applied each period. It's calculated as APR divided by the number of compounding periods per year.
4. **Effective Annual Rate (EAR):** The actual rate at which an investment grows per year. It accounts for intra-year compounding.
Use the following formula to calculate EAR:
\[
\text{EAR} = \left(1 + \frac{\text{APR}}{n}\right)^n - 1
\]
where \( n \) is the number of compounding periods per year.
Complete the tables using the formulas for more precise financial planning and understanding of investment growth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d26b270-cc71-4063-87dd-ee239d290c03%2Fc2b9c990-2b12-49a6-a295-f218b1cb3576%2F33y7o4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Periodic Interest Rates
In the following table, fill in the periodic rates and the effective annual rates (EARs).
#### Table 1: Periodic Rates Calculation
| Period | APR | Compounding per Year | Periodic Rate | Effective Annual Rate |
|-------------|-------|----------------------|---------------|-----------------------|
| Semiannual | 8% | 2 | | |
| Quarterly | 9% | 4 | | |
| Monthly | 7.5% | 12 | | |
| Daily | 4.25% | 365 | | |
**Instructions:** Fill in the periodic rates in the table above. Round to two decimal places.
#### Table 2: Effective Annual Rates Calculation
| Period | APR | Compounding per Year | Periodic Rate | Effective Annual Rate |
|-------------|-------|----------------------|---------------|-----------------------|
| Semiannual | 8% | 2 | 4.00% | |
| Quarterly | 9% | 4 | 2.25% | |
| Monthly | 7.5% | 12 | 0.63% | |
| Daily | 4.25% | 365 | 0.01% | |
**Instructions:** Fill in the effective annual rates in the table above. Round to two decimal places.
---
### Explanation
1. **APR (Annual Percentage Rate):** The annual rate of interest without accounting for compounding within the year.
2. **Compounding per Year:** The number of times interest is applied to the balance in a year.
3. **Periodic Rate:** The interest rate applied each period. It's calculated as APR divided by the number of compounding periods per year.
4. **Effective Annual Rate (EAR):** The actual rate at which an investment grows per year. It accounts for intra-year compounding.
Use the following formula to calculate EAR:
\[
\text{EAR} = \left(1 + \frac{\text{APR}}{n}\right)^n - 1
\]
where \( n \) is the number of compounding periods per year.
Complete the tables using the formulas for more precise financial planning and understanding of investment growth.
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