Nice practical question.
Please tell Sherri that it is less expensive to get a bank loan than to use the credit card.
Principal, P=1050.25
interest rate, i = 18.5%/12 per month
Monthly Repayment, A = 400
We need to calculate the monthly balance to know how many months it takes her to pay off the debit, and hence the interest charge.
As usual, we assume the debit is made at the beginning of the month, and the $400 paid at the end of the month. In actual practice, all these debits and credits are calculated on a daily balance basis, and interest accumulated at the end of the month.
The monthly interest is calculated as the balance from last month multiplied by the interest rate, 18.5%/12. The amount owing (at the end of the month)
F=Balance(1+0.185/12)
month Owing Paid Balance Calculation of owing next month
0 1050.25 0 1050.25 1050.25*(1+0.185/12)=1066.44
1 1066.44 400 666.44 666.44(1+0.185/12)=676.72
2 676.72 400 276.72 276.72(1+0.185/12)=280.98
3 280.98 290.98 ................... loan paid off
Total interest paid = 400+400+290.98 - 1050.25 = 40.73