June has a credit card balance of $4,350 that comes with a 19% APR. She would like to have the balance paid off in the next 8 months, but she is having trouble making the monthly payments required to do so. In order to lower her monthly payments, she decides to sell her porcelain doll collection for $2,000 to apply directly to her credit card balance. June still wants to pay off the balance in 8 months. By applying the doll money, how much has June lowered her minimum monthly payment?
Use the fixed-payment loan formula with monthly interest rate 0.19 ÷ 12 and 8 payments. The monthly payment is proportional to the starting balance, so reducing the balance by $2,000 lowers the payment by $2,000 × [(0.19 ÷ 12) ÷ (1 − (1 + 0.19 ÷ 12)^−8)] ≈ $268.14. Thus the reduction is $268.14, choice B.
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