Math 534

Sara had just rented her first apartment starting December 1 before beginning college in January. The apartment had washer and dryer hook-ups, so Sara wanted to buy the appliances to avoid trips to the laundromat. The Saturday newspaper had an advertisement for a local appliance store offering “90 days, same as cash!” financing. Sara asked how the financing worked and learned that she could pay for the washer and dryer anytime during the first 90 days for the purchase price plus sales tax. If she waited longer, she would have to pay the purchase price, plus sales tax, plus 26.8% annual simple interest for the first 90 days, plus 3% simple interest per month (or any part of a month) on the unpaid balance after 90 days. Together, the washer and dryer cost $699 plus the 8.25% sales tax. Sara knew that her tax refund from the IRS would be $1,000 so she bought the washer and dryer confident that she could pay off the balance within the 90 days.

2. If Sara bought the washer and dryer on December 15, using the exact interest, what is her deadline for paying no interest in a non-leap year? In a leap year? Is the finance company likely to use exact or ordinary interest and why?
December 15th is the 349th day of the year. 365-349=16 days 90-16=74 days. 74 days into the new year is March 15th. March 15th is the latest date to pay interest free in a normal year. You add one day for a leap year so you simply add one to the regular answer and you have March 16th.
I would have to think that the financing would follow the bankers rule and use ordinary interest as it accrues more interest therefore more profit for the business.

4. How much did it cost Sara to pay off this loan 17 days late? What annual simple interest rate does this amount to?
-The orginal cost of the product is $699 with sales tax of 8.25%, 26.8% annual simple interest for 90 days and 3% per month after 90 days on unpaid balance. First multiply $699 by 8.35% sales tax which equals $756.67. Then