Inflation, nominal interest rates, and real rates. Given the following information, . estimate the real rate with the approximate nominal interest rate equation and the true nominal interest rate equation (Fisher effect) for each set of nominal and inflation rates. First, fill in the approximate real interest rate in the following table: (Round to two decimal places.)
Inflation, nominal interest rates, and real rates. Given the following information, . estimate the real rate with the approximate nominal interest rate equation and the true nominal interest rate equation (Fisher effect) for each set of nominal and inflation rates. First, fill in the approximate real interest rate in the following table: (Round to two decimal places.)
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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![**Inflation, Nominal Interest Rates, and Real Rates**
Given the following information, estimate the real rate using both the approximate nominal interest rate equation and the true nominal interest rate equation (Fisher effect) for each set of nominal and inflation rates.
**Approximate Real Interest Rate Table:**
(Round to two decimal places.)
| Nominal Rate | Inflation Rate | Approximate Real Rate |
|--------------|----------------|-----------------------|
| 13.0% | 6.5% | |
| 9.0% | 3.0% | |
| 20.0% | 15.0% | |
| 5.0% | 8.0% | |
**True Real Interest Rate Table:**
(Round to two decimal places.)
| Nominal Rate | Inflation Rate | True Real Rate |
|--------------|----------------|----------------|
| 13.0% | 6.5% | |
| 9.0% | 3.0% | |
| 20.0% | 15.0% | |
| 5.0% | 8.0% | |
**Instructions:**
1. **Approximate Real Rate:** Calculate using the formula:
\[
\text{Approximate Real Rate} = \text{Nominal Rate} - \text{Inflation Rate}
\]
2. **True Real Rate:** Calculate using the Fisher equation:
\[
1 + \text{Nominal Rate} = (1 + \text{Real Rate}) \times (1 + \text{Inflation Rate})
\]
Rearrange to find the real rate.
Use these equations to fill in the tables with calculated values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d76a024-bd52-442b-a28d-e2cd86a37299%2Fa1f3ccb1-2805-4d0c-84e8-41bfee3e5413%2Fi8krjhb_processed.png&w=3840&q=75)
Transcribed Image Text:**Inflation, Nominal Interest Rates, and Real Rates**
Given the following information, estimate the real rate using both the approximate nominal interest rate equation and the true nominal interest rate equation (Fisher effect) for each set of nominal and inflation rates.
**Approximate Real Interest Rate Table:**
(Round to two decimal places.)
| Nominal Rate | Inflation Rate | Approximate Real Rate |
|--------------|----------------|-----------------------|
| 13.0% | 6.5% | |
| 9.0% | 3.0% | |
| 20.0% | 15.0% | |
| 5.0% | 8.0% | |
**True Real Interest Rate Table:**
(Round to two decimal places.)
| Nominal Rate | Inflation Rate | True Real Rate |
|--------------|----------------|----------------|
| 13.0% | 6.5% | |
| 9.0% | 3.0% | |
| 20.0% | 15.0% | |
| 5.0% | 8.0% | |
**Instructions:**
1. **Approximate Real Rate:** Calculate using the formula:
\[
\text{Approximate Real Rate} = \text{Nominal Rate} - \text{Inflation Rate}
\]
2. **True Real Rate:** Calculate using the Fisher equation:
\[
1 + \text{Nominal Rate} = (1 + \text{Real Rate}) \times (1 + \text{Inflation Rate})
\]
Rearrange to find the real rate.
Use these equations to fill in the tables with calculated values.
![**Data Table Overview**
This table allows users to input data into a spreadsheet by clicking on the provided icon. It displays four columns, each representing different financial rates. Here is a detailed breakdown of the table's content:
1. **Nominal Rate**: This column lists the nominal interest rates for different cases. The rates provided are 13.0%, 9.0%, 20.0%, and 5.0%.
2. **Inflation Rate**: This column shows the corresponding inflation rates for each nominal rate. The listed rates are 6.5%, 3.0%, 15.0%, and 8.0%.
3. **Approximate Real Rate**: This column is meant to display the approximate real interest rates, which are currently marked with question marks (?). The approximate real rate is typically calculated using the formula:
\[
\text{Approximate Real Rate} = \text{Nominal Rate} - \text{Inflation Rate}
\]
4. **True Real Rate**: This column is intended to show the true real interest rates, also marked with question marks (?). The true real rate is often calculated using the formula:
\[
\text{True Real Rate} = \frac{1 + \text{Nominal Rate}}{1 + \text{Inflation Rate}} - 1
\]
This table is a useful tool for understanding the relationship between nominal rates, inflation, and real interest rates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d76a024-bd52-442b-a28d-e2cd86a37299%2Fa1f3ccb1-2805-4d0c-84e8-41bfee3e5413%2Fu6efvgj_processed.png&w=3840&q=75)
Transcribed Image Text:**Data Table Overview**
This table allows users to input data into a spreadsheet by clicking on the provided icon. It displays four columns, each representing different financial rates. Here is a detailed breakdown of the table's content:
1. **Nominal Rate**: This column lists the nominal interest rates for different cases. The rates provided are 13.0%, 9.0%, 20.0%, and 5.0%.
2. **Inflation Rate**: This column shows the corresponding inflation rates for each nominal rate. The listed rates are 6.5%, 3.0%, 15.0%, and 8.0%.
3. **Approximate Real Rate**: This column is meant to display the approximate real interest rates, which are currently marked with question marks (?). The approximate real rate is typically calculated using the formula:
\[
\text{Approximate Real Rate} = \text{Nominal Rate} - \text{Inflation Rate}
\]
4. **True Real Rate**: This column is intended to show the true real interest rates, also marked with question marks (?). The true real rate is often calculated using the formula:
\[
\text{True Real Rate} = \frac{1 + \text{Nominal Rate}}{1 + \text{Inflation Rate}} - 1
\]
This table is a useful tool for understanding the relationship between nominal rates, inflation, and real interest rates.
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