TI Calculator Graded Problem Set Like many college students, Elaine applied for and got a credit card that has an annual percentage rate (APR) of 15%. The first thing she did was buy a new DVD player for $250. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of $15. Assume Elaine makes her payment when she sees her statement at the end of each month. If Elaine 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?

Question

Mathematics

Amelie Roberson

16 April, 11:47

TI Calculator Graded Problem Set Like many college students, Elaine applied for and got a credit card that has an annual percentage rate (APR) of 15%. The first thing she did was buy a new DVD player for $250. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of $15. Assume Elaine makes her payment when she sees her statement at the end of each month. If Elaine 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?

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Alissa Harper · Answer 1

Answer:16.667months

Step-by-step explanation:

The interest rate per annum is 15%

So per month is 15%:12months=1.25%/month

So the amount needed to defray the outstanding balance on the credit card will be

1.$15 every month for n months=15n

2. interest rate on outstanding balance=100+1.25=101.25% = (1.0125) ^n where n = number of months

The amount left after n months will be (250-15n) * 1.0125^n

Equating to zero when the $250 is fully paid

250-15n * (1.0125) ^n=0

15n = 250

Dividing both sides by 15

n=250/15. = 16.667months

So it will take 16.667 months for the outstanding balance of $250 incurred to be cleaned up