Suppose that on January 1 you have a balance of $6,000 on the following credit cards, which you want to pay off in the given amount of time. Assume that you make no additional charges to the card after January 1. The credit card APR is 24%, and you want to pay off the balance in 1 year. $ Round to the nearest cent The credit card APR is 25%, and you want to pay off the balance in 2 years. $ Round to the nearest cent The credit card APR is 26 % , and you want to pay off the balance in 3 years. $ Round to the nearest cent
Suppose that on January 1 you have a balance of $6,000 on the following credit cards, which you want to pay off in the given amount of time. Assume that you make no additional charges to the card after January 1. The credit card APR is 24%, and you want to pay off the balance in 1 year. $ Round to the nearest cent The credit card APR is 25%, and you want to pay off the balance in 2 years. $ Round to the nearest cent The credit card APR is 26 % , and you want to pay off the balance in 3 years. $ Round to the nearest cent
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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![### Credit Card Balance Payoff Exercise
#### Hypothetical Scenario:
Suppose that on January 1, you have a balance of $6,000 on the following credit cards, which you aim to pay off within the specified time frames. Assume no additional charges are made to the card after January 1.
1. **Case 1:**
- **APR**: 24%
- **Payoff Period**: 1 year
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
2. **Case 2:**
- **APR**: 25%
- **Payoff Period**: 2 years
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
3. **Case 3:**
- **APR**: 26%
- **Payoff Period**: 3 years
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
#### Explanation:
To find out how much you need to pay each month to pay off your credit card balance within the specified time using a given APR (Annual Percentage Rate), you can use the following formula:
\[ \text{Monthly Payment} = P \frac{r(1+r)^n}{(1+r)^n-1} \]
Where:
- \(P\) is the principal loan amount ($6,000)
- \(r\) is the monthly interest rate (APR divided by 12)
- \(n\) is the number of months
Let's calculate the monthly payment for each scenario.
##### Case 1: Paying off in 1 year (12 months)
- Principal (P) = $6,000
- APR = 24% → Monthly interest rate (r) = 24%/12 = 2% or 0.02
- Number of months (n) = 12
##### Case 2: Paying off in 2 years (24 months)
- Principal (P) = $6,000
- APR = 25% → Monthly interest rate (r) = 25%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e14e833-b473-4144-adde-e217b311654e%2Fcab49627-ee9a-4262-8a90-ee8054658d52%2F2y2e1ec_processed.png&w=3840&q=75)
Transcribed Image Text:### Credit Card Balance Payoff Exercise
#### Hypothetical Scenario:
Suppose that on January 1, you have a balance of $6,000 on the following credit cards, which you aim to pay off within the specified time frames. Assume no additional charges are made to the card after January 1.
1. **Case 1:**
- **APR**: 24%
- **Payoff Period**: 1 year
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
2. **Case 2:**
- **APR**: 25%
- **Payoff Period**: 2 years
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
3. **Case 3:**
- **APR**: 26%
- **Payoff Period**: 3 years
- **Monthly Payment Calculation**: \(\text{Monthly Payment} = $ \_\_\_\_\_\_\_\_\_\_\_\_)
- *Round to the nearest cent*
#### Explanation:
To find out how much you need to pay each month to pay off your credit card balance within the specified time using a given APR (Annual Percentage Rate), you can use the following formula:
\[ \text{Monthly Payment} = P \frac{r(1+r)^n}{(1+r)^n-1} \]
Where:
- \(P\) is the principal loan amount ($6,000)
- \(r\) is the monthly interest rate (APR divided by 12)
- \(n\) is the number of months
Let's calculate the monthly payment for each scenario.
##### Case 1: Paying off in 1 year (12 months)
- Principal (P) = $6,000
- APR = 24% → Monthly interest rate (r) = 24%/12 = 2% or 0.02
- Number of months (n) = 12
##### Case 2: Paying off in 2 years (24 months)
- Principal (P) = $6,000
- APR = 25% → Monthly interest rate (r) = 25%
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