Math Problem Statement

Paying Off a Credit Card You owe $8000 on a credit card. Because of the high balance, you stop charging and begin paying off the card. You can afford to make only the minimum monthly payment, which is 5% of the balance. The card carries an APR of 24%. Under these conditions, the remaining balance after t monthly payments is given by B= 8000(1.02 times 0.95) exponent t dollars. You feel comfortable resuming charging with the card when the balance is between $1000 and $2000. a. Plot the graph of B along with the target values of 1000 and 2000. Use a horizontal span of 0 to 100.

Solution

Here is the graph showing the remaining credit card balance B(t)B(t) over time, along with the target values of $1000 and $2000. The balance decreases as monthly payments are made, but due to the compounding interest, it takes time to reach those lower balances.

Would you like further details or have any questions?

Here are some related questions you might find helpful:

  1. How long will it take to reach a balance below $2000?
  2. How is the monthly interest of 2% derived from the APR of 24%?
  3. What happens to the balance if the monthly payment percentage is increased?
  4. How would the graph change if the APR was higher or lower?
  5. How can you calculate the total interest paid over the repayment period?

Tip: Increasing your monthly payment above the minimum can drastically reduce the time it takes to pay off a loan, saving money on interest in the long run.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponential Decay
Financial Mathematics

Formulas

B = 8000(1.02 * 0.95)^t

Theorems

-

Suitable Grade Level

Grades 10-12

Related Recommendation

Credit Card Balance Calculation with 22% APR and 3% Minimum Payment

Credit Card Balance Reduction Over Time Using Exponential Decay

Paying Off a Credit Card with 24% APR: How Long Until the Balance is Between $1000 and $2000?

Exponential Regression Model for Predicting Credit Card Debt Growth

Solve Exponential Decay for Credit Card Payments Using Logarithms