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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Use Table 12-2 to find how much should be deposited now at 6% interest, compounded monthly, to yield an
![The table titled "Periods and Interest Rates" provides a detailed breakdown of interest rates over a range of periods from 1 to 36. Each column represents a different interest rate, ranging from 9% to 18%.
### Table Explanation:
- **Top Row:** Indicates the interest rates from 9% to 18% and period identifiers.
- **First Column and Last Row:** Lists the period numbers from 1 to 36.
- **Data Cells:** Contain the calculated values for each period and interest rate combination, rounded to five decimal places.
### Values Description:
The values in this table were generated using the formula:
\[ \frac{(1+i)^n - 1}{i(1+i)^n} \]
- **i:** Interest rate per period.
- **n:** Total number of periods.
### Usage:
This table is useful for financial calculations involving compounded interest over multiple periods. It allows the user to quickly locate the value corresponding to a specific interest rate and period combination for projected financial assessments or comparisons.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd201cd7c-f0d9-4cde-8ad3-a66bd40ce2a0%2F8f41f8bf-dd5e-4b41-ab34-d626bf926eba%2Fup2swxm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The table titled "Periods and Interest Rates" provides a detailed breakdown of interest rates over a range of periods from 1 to 36. Each column represents a different interest rate, ranging from 9% to 18%.
### Table Explanation:
- **Top Row:** Indicates the interest rates from 9% to 18% and period identifiers.
- **First Column and Last Row:** Lists the period numbers from 1 to 36.
- **Data Cells:** Contain the calculated values for each period and interest rate combination, rounded to five decimal places.
### Values Description:
The values in this table were generated using the formula:
\[ \frac{(1+i)^n - 1}{i(1+i)^n} \]
- **i:** Interest rate per period.
- **n:** Total number of periods.
### Usage:
This table is useful for financial calculations involving compounded interest over multiple periods. It allows the user to quickly locate the value corresponding to a specific interest rate and period combination for projected financial assessments or comparisons.
![**Table 12-2: Present Value of an Annuity of 1 Per Period**
The table lists the present value of an annuity for different interest rates and periods, represented as a grid of numbers. Each row corresponds to a number of periods, ranging from 1 to 36. Each column represents an interest rate, ranging from 1% to 8%.
**Columns:**
- **Interest Rates**: 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%
**Rows:**
- **Periods**: 1 to 36
**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. Each value is rounded to five decimal places.
**Example Values:**
- For a 5% interest rate over 10 periods, the present value is 7.72173.
- For a 3% interest rate over 20 periods, the present value is 14.87747.
This table is useful for calculating the present value of an annuity, which helps in financial planning and investment evaluations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd201cd7c-f0d9-4cde-8ad3-a66bd40ce2a0%2F8f41f8bf-dd5e-4b41-ab34-d626bf926eba%2F9kg6l8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Table 12-2: Present Value of an Annuity of 1 Per Period**
The table lists the present value of an annuity for different interest rates and periods, represented as a grid of numbers. Each row corresponds to a number of periods, ranging from 1 to 36. Each column represents an interest rate, ranging from 1% to 8%.
**Columns:**
- **Interest Rates**: 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%
**Rows:**
- **Periods**: 1 to 36
**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. Each value is rounded to five decimal places.
**Example Values:**
- For a 5% interest rate over 10 periods, the present value is 7.72173.
- For a 3% interest rate over 20 periods, the present value is 14.87747.
This table is useful for calculating the present value of an annuity, which helps in financial planning and investment evaluations.
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