622 CHAPTER 10 Consumer Mathematics money until the date you repay the money. When you make purchases or obtain cash advances, the minimum monthly payment will generally be any new fees and interest plus at least 1% of the outstanding principal. This sum is then rounded up to the nearest whole dollar. Credit card companies often have $20 as the lowest possible minimum monthly payment. These guidelines will vary among the different credit card companies. If you currently have a credit card, you can determine how your minimum monthly payment is calculated by reading the back of your monthly statement or by reading the literature given to you when you obtained the credit card. Example 7 Calculating the Minimum Monthly Payments Luciana’s credit card company determines her minimum monthly payment by adding any new interest to 1.2% of the outstanding principal. The credit card company charges an interest rate of 0.05271% per day for purchases. On April 15, Luciana used her credit card to purchase a new recliner and sofa for $3800. She made no other purchases in April. a) Assuming Luciana owed no interest, determine her minimum payment due on May 1, her billing date. b) On May 1, instead of making the minimum payment, Luciana makes a payment of $950. Assuming there are no additional charges or cash advances, determine her minimum payment due on June 1. Solution a) Since there is no new interest due, Luciana’s minimum monthly payment due on May 1 is determined by taking 1.2% of the outstanding principal, or 0.012 $3800 $45.60. × = Rounding up to the nearest whole dollar, we determine that her minimum monthly payment is $46. b) Luciana’s minimum monthly payment due on June 1 will be the sum of the new interest plus 1.2% of her outstanding principal. To calculate her new interest charges, we will use the simple interest formula, i prt. = The principal is $3800 $950 $2850; − = the rate r is 0.05271%, or 0.0005271 per day, and the time is 31 days since May has 31 days. i prt $2850 0.0005271 31 $46.57 = = × × ≈ To determine 1.2% of the outstanding principal, multiply 0.012 by $2850 to get $34.20. Next we add the new interest, $46.57, to 1.2% of the outstanding principal, $34.20, to get $34.20 $46.57 $80.77. + = Rounding up to the nearest whole dollar, we determine that Luciana’s minimum monthly payment on June 1 is $81. 7 Now try Exercise 31 In Example 7, Luciana made no additional charges during the month. When additional charges are made during the month, the finance charges on open-end installment loans or credit cards are generally calculated in one of two ways: the previous balance method or the average daily balance method. Example 8 illustrates the previous balance method, and Example 9 illustrates the average daily balance method. With the previous balance method, the borrower is charged interest or a finance charge on the previous balance from the previous charge period. Example 8 Finance Charges Using the Previous Balance Method In October, Peter charged all the supplies for his Halloween party to his Visa card. On November 5, the billing date, Peter had a balance due of $275. From November 5 through December 4, he did some shopping and charged items totaling $320, and he also made a payment of $145. DGLimages/Shutterstock
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