Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
Be sure to include in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
Let's first calculate the monthly interest rate on the credit card, and then solve parts a. and b. of the problem.
1. Monthly interest rate on the credit card:
APR = 13.6%
Monthly interest rate = APR / 12 = 13.6% / 12 = 1.13333...%
a. If you only put half of the available money ($150) toward the credit card each month:
Let X be the number of months to pay off the credit card balance.
Using the formula for compound interest:
754.43(1 + 0.0133)^X - 150X = 0
Solving this equation, it would take approximately 7 months to pay off the credit card.
b. If you put all of the available money ($300) toward the credit card each month:
Let Y be the number of months to pay off the credit card balance.
Using the same formula for compound interest:
754.43(1 + 0.0133)^Y - 300Y = 0
Solving this equation, it would take approximately 4 months to pay off the credit card.
Therefore,
a. It would take approximately 7 months to pay off the credit card by putting half of the available money toward it each month.
b. It would take approximately 4 months to pay off the credit card by putting all of the available money toward it each month.