Question

Suppose your credit card balance is ​$15 comma 500. The minimum payment is ​$344​, and the annual percentage rate is 19.6​%.

a.  If you make a constant monthly payment of ​$344​, how long will it take you to pay off the credit card​ balance?

b.  How much interest will you pay if you elect to make the minimum​ payment?

Answer 1

- Credit Card balance = $15,500

a). Minimum monthly payment = $344

Annual percentage rate(APR) = 19.6%

Calculating the time it will to take to pay off the Loan balance:-

Where, P = Credit card balance = $15,500

r = Periodic Interest rate = 19.6%/12 =1.633%

n= no of periods

EMI = Minimum monthly payment = $344

1.35878868(1.016333)^n - 1.35878868 = (1.016333)^n

0.35878868(1.016333)^n = 1.35878868

(1.016333)^n = 3.78715594

Taking log on both sides..

nLog(1.016333) = Log(3.78715594)

n(0.007036027) = 0.578313188

n = 82.19 monthly payments.

So, it will take 82 monthly payments to pay off the credit card balance.

b). Interest Payment = (Minimum monthly payment*No. of Monthly Payments) - Credit card balance

= ($344*82) -$15500

= $ 12,708

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