Due to poor spending habits, Ricky has accumulated $10,000 in credit card debt. He has missed...

Question:

Due to poor spending habits, Ricky has accumulated $10,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 18.95%! If he pays $175 per month on the card, how long will it take Ricky to pay off the card?

Paying off Credit Loans:

Credit card balances usually carry a very high interest rate. For this reason, paying off credit balance sooner could yield substantial savings in interest costs.

Answer and Explanation:

It will take Ricky about 149 months to pay off the card.

We can use the following formula to compute the monthly payment for a loan with principal {eq}P {/eq}, monthly interest rate {eq}r{/eq} and number of monthly payments {eq}T{/eq}:

  • {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

In this question, we know the monthly payment is 175, instead we try to find the number of payments such that the monthly payment calculated using the above formula is exactly equal to 175, which requires solving the following equation:

  • {eq}\displaystyle \frac{10,000*18.95\%/12}{1 - (1 + 18.98\%/12)^{-T}} = 175\\ 1 - (1 + 18.95\%/12)^{-T} = 0.9023809524\\ (1 + 18.95\%/12)^{-T} = 0.09761904762\\ T = 148.50 {/eq}

That is, it takes Ricky at least 149 months to pay off the loan.


Learn more about this topic:

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Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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