624 CHAPTER 10 Consumer Mathematics The calculations in Example 9 are tedious. These calculations, however, are made almost instantaneously with computers. Example 10 illustrates how a credit card may be used to borrow money. (ii) Determine the number of days that the balance did not change between each transaction. Count the first day in the period but not the last day. Note that the time period from July 28 through August 1, the beginning of the next billing cycle, is 4 days. (iii) Multiply the balance due by the number of days the balance did not change. (iv) Determine the sum of the products. Date (i) Balance Due (ii) Number of Days Balance Did Not Change (iii) (Balance)(Days) July 1 $375.80 4 ($375.80)(4) $1503.20 = July 5 $225.80 5 ($225.80)(5) $1129.00 = July 10 $300.15 8 ($300.15)(8) $2401.20 = July 18 $423.65 10 ($423.65)(10) $4236.50 = July 28 $466.15 4 ($466.15)(4) $1864.60 = 31 (iv) Sum $11,134.50 = (v) Divide this sum by the number of days in the billing cycle (in the month). The number of days may be determined by adding the days in column (ii). $11,134.50 31 $359.18 = Thus, the average daily balance is $359.18. b) The finance charge for the month is determined using the simple interest formula with the average daily balance as the principal. i $359.18 0.013 1 $4.67 = × × = c) Since the finance charge for the month is $4.67, the balance owed on August 1 is $466.15 $4.67, + or $470.82. 7 Now try Exercise 39 Example 10 Credit Card Cash Advance Thomasina wishes to purchase an antique bookcase for $1500. Since the antique dealer accepts cash only, Thomasina uses her credit card to obtain a cash advance of $1500. She borrowed the money on July 10 and repaid it on July 31. If Thomasina is charged an interest rate of 0.06164% per day, how much did Thomasina have to repay the credit card company on July 31? Solution The amount Thomasina pays is the original principal, $1500, plus any accrued interest. Interest on cash advances is generally calculated for the exact number of days of the loan, starting with the day the money is obtained. The time of this loan is 21 days. Using the simple interest formula, we get the following: i prt $1500 0.0006164 21 $19.42 = = × × ≈ Therefore, on July 31, Thomasina must repay the credit card company $1500 $19.42 $1519.42. + = 7 Now try Exercise 43 Elena Elisseeva/Shutterstock
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