Question

"You currently owe $2480 on your credit card, which calculates interest based on 18.23% APR, compounded daily. You make quarterly payments of $724 at the end of every quarter, and you make your first payment exactly one quarter from now. How many quarters until you pay off your credit card debt? Assume 91 days in each quarter. Express your answer as an integer (number of quarters)."

Answer 1

Annual Percentage Rate (APR) = 18.23%

Daily Percentage Rate (DPR) = 18.23%/365 = 0.050%

Now, since the payment is done every quarter and the interest is compounded daily, we will take our calculation time as 91 days (as given in the question) Therefore, (T) = 91 days

Total Amount Due (A) = $2480

Quarterly Payment (Q) = Interest accrued (I) + Principal payment (P)

Quarterly Payment (Q) = $724

Interest Accrued can be calculated using the formula (I) = A*(((1+DPR)^T)-1)

For first quarter,

I = 2480*(((1+0.050)^91)-1) = 115.29

Hence,

Q = I + P

P = Q – I

Which gives us

P = 724 – 115.29 = 608.71

Subtracting the paid principle from the due amount, we get the Total Amount due (A) for the second quarter as $1871.29.

Please find below a table containing the entire calculation for each quarters.

As we can see, for the fourth quarter, Total Outstanding amount is $567.66. Hence with the payment of $594.04 in the fourth quarter, the credit card debt would be completely paid off.

Hence number of quarters required for paying off credit card debt = 4

Hope this answers your question.