2-2 to calculate the present value (in $) of the annuity due. (Round your answer to the nearest cent.) Annuity Payment Payment Frequency Time Period (years) Nominal Rate (%) Interest Compounded Present Value of the Annuity $400 every month 2 1/4
2-2 to calculate the present value (in $) of the annuity due. (Round your answer to the nearest cent.) Annuity Payment Payment Frequency Time Period (years) Nominal Rate (%) Interest Compounded Present Value of the Annuity $400 every month 2 1/4
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
Related questions
Question
100%
Use Table 12-2 to calculate the present value (in $) of the annuity due. (Round your answer to the nearest cent.)
| Annuity Payment |
Payment Frequency |
Time Period (years) |
Nominal Rate (%) |
Interest Compounded |
Present Value of the Annuity |
||
|---|---|---|---|---|---|---|---|
| $400 | every month | 2 1/4
|
6 | monthly | $ |
![The image contains a detailed table showing values for compound interest rates over varying periods and rates. Below is the transcription and description of the content:
### Table: Compound Interest Rate Values
#### Columns:
1. **Period**: Ranges from 1 to 36.
2. **Interest Rates (1% to 8%)**: Displays calculated values across different interest rates starting from 1% to 8%.
#### Rows:
The table includes calculated interest amounts for each period, from 1 to 36 periods, for each interest rate indicated in the column headers (1% through 8%). For example:
- For a period of 1 year and an interest rate of 1%, the value is 0.99052.
- For a period of 2 years and an interest rate of 2%, the value is 1.97040.
- This pattern continues throughout, illustrating the compounding effect over time.
#### Formula:
The values in the table are generated using the formula:
\[
\frac{(1+i)^n - 1}{i(1+i)^n}
\]
where **i** is the interest rate per period, and **n** is the total number of periods. Values are rounded to five decimal places.
### Explanation:
- The table is structured to help understand the impact of compound interest over a set number of periods and different interest rates.
- The more the periods or the higher the interest rates, the greater the compounding effect on the initial principal.
- By using the given formula, one can calculate the future value of an investment or loan.
This table is often used in financial studies to illustrate how compound interest works across different time frames and rates, showing the growth of an investment over time compared to simple interest calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd201cd7c-f0d9-4cde-8ad3-a66bd40ce2a0%2Ff5688910-19be-48e9-881a-75f121e2d73e%2Fjgvhd5c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a detailed table showing values for compound interest rates over varying periods and rates. Below is the transcription and description of the content:
### Table: Compound Interest Rate Values
#### Columns:
1. **Period**: Ranges from 1 to 36.
2. **Interest Rates (1% to 8%)**: Displays calculated values across different interest rates starting from 1% to 8%.
#### Rows:
The table includes calculated interest amounts for each period, from 1 to 36 periods, for each interest rate indicated in the column headers (1% through 8%). For example:
- For a period of 1 year and an interest rate of 1%, the value is 0.99052.
- For a period of 2 years and an interest rate of 2%, the value is 1.97040.
- This pattern continues throughout, illustrating the compounding effect over time.
#### Formula:
The values in the table are generated using the formula:
\[
\frac{(1+i)^n - 1}{i(1+i)^n}
\]
where **i** is the interest rate per period, and **n** is the total number of periods. Values are rounded to five decimal places.
### Explanation:
- The table is structured to help understand the impact of compound interest over a set number of periods and different interest rates.
- The more the periods or the higher the interest rates, the greater the compounding effect on the initial principal.
- By using the given formula, one can calculate the future value of an investment or loan.
This table is often used in financial studies to illustrate how compound interest works across different time frames and rates, showing the growth of an investment over time compared to simple interest calculations.
![### Educational Resource: Compound Interest Table
#### Overview
The table provides compound interest factors for different interest rates and periods. It is designed to help calculate the future value of an investment when interest is compounded annually.
#### Table Structure
- **Columns:** Represent different annual interest rates from 9% to 18%.
- **Rows (Periods):** Range from 1 to 36 periods, signifying the number of years or compounding periods.
#### Key Features
- **Interest Rates:** Each column under the interest rates (9% to 18%) provides the compound interest factor for that rate over a specific period (year).
- **Periods:** The column on the left indicates periods from 1 to 36. The same values are mirrored on the far right of the table for easy reference.
- **Compound Interest Factors:** Calculated using the formula:
\[
\text{Factor} = \frac{(1 + i)^n - 1}{i(1 + i)^n}
\]
Where:
- \( i \) = interest rate per period (expressed as a decimal)
- \( n \) = total number of periods
These values are rounded to five decimal places.
#### Application
Use this table to find the future value of an investment for a specific interest rate and period. Multiply the initial investment by the corresponding factor from the table to get the compounded amount.
#### Additional Information
This table serves as a practical tool in finance to simplify the process of calculating the effects of compound interest over time, thus aiding in investment planning and analysis.
Each value in the table informs users about how much one unit of currency is worth after compounding annually at the respective rate for the specified number of years.
By employing these factors, financial analysts and students can effortlessly derive the future value without complex calculations, facilitating more efficient decision-making in financial forecasting and budgeting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd201cd7c-f0d9-4cde-8ad3-a66bd40ce2a0%2Ff5688910-19be-48e9-881a-75f121e2d73e%2F3euxgt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Compound Interest Table
#### Overview
The table provides compound interest factors for different interest rates and periods. It is designed to help calculate the future value of an investment when interest is compounded annually.
#### Table Structure
- **Columns:** Represent different annual interest rates from 9% to 18%.
- **Rows (Periods):** Range from 1 to 36 periods, signifying the number of years or compounding periods.
#### Key Features
- **Interest Rates:** Each column under the interest rates (9% to 18%) provides the compound interest factor for that rate over a specific period (year).
- **Periods:** The column on the left indicates periods from 1 to 36. The same values are mirrored on the far right of the table for easy reference.
- **Compound Interest Factors:** Calculated using the formula:
\[
\text{Factor} = \frac{(1 + i)^n - 1}{i(1 + i)^n}
\]
Where:
- \( i \) = interest rate per period (expressed as a decimal)
- \( n \) = total number of periods
These values are rounded to five decimal places.
#### Application
Use this table to find the future value of an investment for a specific interest rate and period. Multiply the initial investment by the corresponding factor from the table to get the compounded amount.
#### Additional Information
This table serves as a practical tool in finance to simplify the process of calculating the effects of compound interest over time, thus aiding in investment planning and analysis.
Each value in the table informs users about how much one unit of currency is worth after compounding annually at the respective rate for the specified number of years.
By employing these factors, financial analysts and students can effortlessly derive the future value without complex calculations, facilitating more efficient decision-making in financial forecasting and budgeting.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education