Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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![Title: Understanding Credit Card Interest Calculations
---
**Problem Statement:**
Janet borrows $3,800 from a credit card company at an annual interest rate of 24.5% for 3 years. Determine Janet’s monthly payment.
**Explanation:**
In this problem, Janet needs to determine her monthly payment for a loan borrowed with a specific interest rate. To solve this, you would typically use the formula for calculating the monthly payment on an installment loan:
\[ \text{M} = \frac{\text{P} \times \text{r} \times (1+\text{r})^n}{(1+\text{r})^n-1} \]
Where:
- \( \text{M} \) is the monthly payment.
- \( \text{P} \) is the principal amount ($3,800).
- \( \text{r} \) is the monthly interest rate (annual rate divided by 12 months).
- \( n \) is the number of payments (months).
---
**Steps to Solution:**
1. **Convert the annual interest rate to a monthly rate.**
\[ \text{Monthly rate} = \frac{24.5\%}{12} = 2.0417\% \text{, or } 0.020417 \text{ in decimal} \]
2. **Determine the number of monthly payments.**
For 3 years:
\[ n = 3 \times 12 = 36 \text{ months} \]
3. **Substitute these values into the formula and calculate the monthly payment.**
**Graph/Diagram Explanation:**
There is no graph or diagram accompanying this problem. If one were to be included, it could visually represent the decreasing balance of the loan over time as payments are made, leading to an understanding of how principal and interest components affect the total payment amount each month.
---
**Conclusion:**
This exercise aids in understanding how monthly payments are structured for loans and credit agreements, emphasizing the significance of interest rates and payment schedules in financial planning.](https://content.bartleby.com/qna-images/question/8946c7ff-a7db-4ece-95ac-6256e20973be/820b8b11-6513-45bc-bc32-da689df1a3bd/kw5b7z8_processed.jpeg)
Transcribed Image Text:Title: Understanding Credit Card Interest Calculations
---
**Problem Statement:**
Janet borrows $3,800 from a credit card company at an annual interest rate of 24.5% for 3 years. Determine Janet’s monthly payment.
**Explanation:**
In this problem, Janet needs to determine her monthly payment for a loan borrowed with a specific interest rate. To solve this, you would typically use the formula for calculating the monthly payment on an installment loan:
\[ \text{M} = \frac{\text{P} \times \text{r} \times (1+\text{r})^n}{(1+\text{r})^n-1} \]
Where:
- \( \text{M} \) is the monthly payment.
- \( \text{P} \) is the principal amount ($3,800).
- \( \text{r} \) is the monthly interest rate (annual rate divided by 12 months).
- \( n \) is the number of payments (months).
---
**Steps to Solution:**
1. **Convert the annual interest rate to a monthly rate.**
\[ \text{Monthly rate} = \frac{24.5\%}{12} = 2.0417\% \text{, or } 0.020417 \text{ in decimal} \]
2. **Determine the number of monthly payments.**
For 3 years:
\[ n = 3 \times 12 = 36 \text{ months} \]
3. **Substitute these values into the formula and calculate the monthly payment.**
**Graph/Diagram Explanation:**
There is no graph or diagram accompanying this problem. If one were to be included, it could visually represent the decreasing balance of the loan over time as payments are made, leading to an understanding of how principal and interest components affect the total payment amount each month.
---
**Conclusion:**
This exercise aids in understanding how monthly payments are structured for loans and credit agreements, emphasizing the significance of interest rates and payment schedules in financial planning.
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