You have a credit card that has a balance of $6680$⁢6680 at an APR of 19.49%19.49%. You plan to pay $300$⁢300 each month in an effort to clear the debt quickly. How many months will it take you to pay off the balance?

To determine how many months it will take to pay off the credit card balance, we can use the formula for paying off a loan with monthly payments and interest:

\[
M = \frac{\log \left(\frac{P}{P - r \times B}\right)}{\log (1 + r)}
\]

Where:
- $ M $ is the number of months it will take to pay off the balance.
- $ B $ is the initial balance ($6680).
- $ r $ is the monthly interest rate, which is the APR divided by 12.
- $ P $ is the monthly payment ($300).
- APR is 19.49%, which means the monthly interest rate is:

\[
r = \frac{19.49}{100 \times 12} = 0.01624
\]

Now let's substitute the values and calculate $ M $.It will take approximately 28 months to pay off the balance of \$6,680 at an APR of 19.49% if you make monthly payments of \$300.

Would you like further details or have any questions about the process? 

Here are 5 related questions to explore:
1. How much total interest will you pay by the end of 28 months?
2. What happens if you increase your monthly payment to \$400?
3. How would the payment duration change if the APR were lower, say 15%?
4. What if you made a one-time payment of \$1,000? How would that affect the timeline?
5. Can you calculate the remaining balance after 12 months?

**Tip**: Making extra payments towards the principal reduces the interest you pay over time, shortening the duration of the loan.

You have a credit card that has a balance of $6680 at an APR of 19.49%. You plan to pay $300 each month in an effort to clear the debt quickly. How many months will it take you to pay off the balance?

Calculate how many months it will take to pay off a $6680 credit card balance with a 19.49% APR and $300 monthly payments. Understand the math behind loan repayment using logarithmic formulas, interest calculations, and algebraic concepts. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation