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Assume that you have a balance of $2800 on your Discover credit card and that you make no more charges. Assume that Discover charges 21% APR and that each month you make only the minimum payment of 2% of the balance. Find how many months it will take to bring the remaining balance down to $2500. (Round your answer to the nearest whole number.)

 =   months

 Oct 17, 2019
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Solution:

 

Preface:Normally these payments are tabulated by using a spreadsheet; however, because there are no additional charges to the card, it is easy to calculate a fixed formula by adjusting the payment percentage rate of (2.0%) by the periodic interest rate.The monthly interest rate is 21.0%12=1.75%(0.0175)The balance before the payment is found by multiplying the previous month's balance by (1.0175). The new balance after payment is 98% of the previous balance and accrued interest. Balance after payment is (B(1.01750.98)) or (B(0.99715). The adjusted fixed payment rate complement is (0.99715). By taking integer multiples of the adjusted fixed payment rate complement and multiplying by the starting balance, the balance for any month(t) is given by:B(t)=2800(0.99715t)

Using this formula, solve for t when (2800(0.99715t))=250028000.99715t2800=250028000.99715t=2528log(0.99715t)=log(2528)tlog(0.9972)= log(2528)t=log(2528)log(0.99715)t=39.71 and t=40 After the 40th payment, the balance will be below 2500 dollars.

 

 

GA

 Oct 17, 2019
edited by GingerAle  Oct 17, 2019
edited by GingerAle  Oct 17, 2019

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