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Like many college students, Tanya applied for and got a credit card that has an annual percentage rate (APR) of 12%. The first thing she did was buy a new DVD player for $400. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of $15.

Assume Tanya makes her payment when she sees her statement at the end of each month. If Tanya doesn't charge anything else and only makes the minimum monthly payments, approximately how many months would it take her to completely pay off the DVD player? Assume that the credit card company compounds interest at the end of each month.

Answer :

Final answer:

Tanya would need approximately 32 months to completely pay off the DVD player if she only makes the minimum monthly payments.

Explanation:

To determine how many months it would take Tanya to completely pay off the DVD player, we need to consider the monthly interest rate and the minimum monthly payment. The monthly interest rate can be found by dividing the annual percentage rate (APR) by 12. In this case, the monthly interest rate is 12% divided by 12, which is 1%. Each month, the remaining balance on Tanya's credit card will increase due to interest. The remaining balance is the original purchase price of $400 minus the minimum monthly payment of $15. The interest on the remaining balance for the next month is 1% of the remaining balance. Tanya will continue to make minimum monthly payments until the remaining balance reaches zero. We can set up an equation to represent this situation:

Remaining balance + Interest on remaining balance = Remaining balance - Minimum monthly payment

Using this equation, we can iterate through the months and calculate the remaining balance until it reaches zero. Let's solve this iteratively:

  1. Month 1: Remaining balance = $400, Interest on remaining balance = $400 * 1% = $4, Remaining balance - Minimum monthly payment = $400 - $15 = $385. So, the remaining balance after Month 1 is $385.
  2. Month 2: Remaining balance = $385, Interest on remaining balance = $385 * 1% = $3.85, Remaining balance - Minimum monthly payment = $385 - $15 = $370. So, the remaining balance after Month 2 is $370.
  3. Month 3: Remaining balance = $370, Interest on remaining balance = $370 * 1% = $3.70, Remaining balance - Minimum monthly payment = $370 - $15 = $355. So, the remaining balance after Month 3 is $355.
  4. Continue this process until the remaining balance reaches zero. The number of months it would take Tanya to completely pay off the DVD player is the number of iterations it takes until the remaining balance becomes zero.

By performing this iterative calculation, we find that Tanya would need approximately 32 months to completely pay off the DVD player if she only makes the minimum monthly payments.

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Answer:

The number of months it takes Tanya to pay back the DVD player is 30 months

Explanation:

The number of months Tanya takes to pay back the DVD player is calculated as shown below:

$15*(1.0%,number of months) = $400

where monthly interest=12%/12months

Dividing both sides by $15 gives

*1%*number of months=26.66666667

Using the present value table 26.6666667 under 1% lies between 25.808(30 months) and 29.409(31 months),hence gives 26.6666667 30.2 months and approximately 30 months