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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![**Equation Use and Variable Explanation**
**Text:**
Please explain when you would use the following equation and also explain what each variable represents.
\[ P = \frac{B \cdot \frac{r}{n}}{\left(1 + \frac{r}{n}\right)^{nt} - 1} \]
**Explanation:**
This equation is used to calculate the regular payment amount \( P \) when paying off a loan or investment over time with regular, constant payments and interest that compounds at regular intervals. It is a form of the annuity payment formula.
- **Variables:**
- \( P \): Payment amount per period.
- \( B \): Initial principal or balance.
- \( r \): Annual interest rate (as a decimal).
- \( n \): Number of compounding periods per year.
- \( t \): Total number of years.
The equation accounts for the compounding of interest, adjusting the annual rate to reflect the frequency of compounding periods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f11c24-8a8a-4185-8b00-606d299e598d%2Fc4d134e8-89d2-4bf1-8d73-551c7bbf7327%2Fs11egq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation Use and Variable Explanation**
**Text:**
Please explain when you would use the following equation and also explain what each variable represents.
\[ P = \frac{B \cdot \frac{r}{n}}{\left(1 + \frac{r}{n}\right)^{nt} - 1} \]
**Explanation:**
This equation is used to calculate the regular payment amount \( P \) when paying off a loan or investment over time with regular, constant payments and interest that compounds at regular intervals. It is a form of the annuity payment formula.
- **Variables:**
- \( P \): Payment amount per period.
- \( B \): Initial principal or balance.
- \( r \): Annual interest rate (as a decimal).
- \( n \): Number of compounding periods per year.
- \( t \): Total number of years.
The equation accounts for the compounding of interest, adjusting the annual rate to reflect the frequency of compounding periods.
Expert Solution
Step 1
Annuity is number of payments which are equal in size and made in equal interval of time.
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