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 day 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 2% simple interest per month on the unpaid balance after 90 days, with minimum payment of $50 per month after the 90-day period. 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.
1. If Sara pays off the balance within 90 days how much will she pay?
2. If Sara bought the washer and dryer on December 15, using the exact interest, what is her deadline for paying no interest is a non-leap year? In a leap year? Is finance company likely to use exact or ordinary interest and why?
3. If Sara’s IRS refund does not come until April 1, what is her payoff amount? (Assume ordinary interest and a non-leap year.)
4. How much did it cost her to pay off this loan 17 day later? What annual simple interest rate does this amount to?
1. To calculate the amount Sara will pay if she pays off the balance within 90 days, we need to add the purchase price of the washer and dryer to the sales tax.
The purchase price of the washer and dryer is $699, and the sales tax is 8.25% of the purchase price.
Sales tax = 8.25% of $699 = $699 * 0.0825 = $57.68
Total amount Sara will pay within 90 days = Purchase price + Sales tax
= $699 + $57.68 = $756.68
Sara will pay $756.68 if she pays off the balance within 90 days.
2. To determine Sara's deadline for paying no interest if she bought the washer and dryer on December 15, we need to consider the 90-day financing term.
In a non-leap year, there are 365 days. Sara bought the appliances on December 15, so she has 15 days in December, plus 31 days in January, and 28 days in February (ignoring leap years).
Deadline for paying no interest in a non-leap year = December 15 + 15 days + 31 days + 28 days = February 28.
In a leap year, there are 366 days. If it is a leap year, the deadline for paying no interest would be February 29.
Regarding whether the finance company is likely to use exact or ordinary interest, it depends on the terms and conditions provided by the finance company. However, in most cases, finance companies use ordinary interest because it simplifies the calculations.
3. If Sara's IRS refund does not come until April 1, we can calculate her payoff amount within this scenario. Assuming ordinary interest and a non-leap year:
Days from December 15 to April 1 = 15 days in December + 31 days in January + 28 days in February + 31 days in March + 1 day in April (up to April 1) = 106 days
Since Sara did not pay off the balance within 90 days, she will have to pay interest on the unpaid balance. The interest rate for the first 90 days is 26.8% annually. To calculate the interest for 90 days:
Interest for 90 days = (26.8% / 365) * $699 * 90
After 90 days, she will be charged an additional 2% per month on the unpaid balance. Since she will be paying on April 1, she will have a total of 106 days without paying the balance. To calculate the interest for the remaining days:
Interest for remaining days = (2% / 365) * $699 * 106
Total interest = Interest for 90 days + Interest for remaining days
The payoff amount = Purchase price + Sales tax + Total interest
4. To calculate the cost of paying off the loan 17 days later, we need to consider the additional interest for those 17 days.
Using the same formulas for calculating interest as in question 3, we can calculate the interest for the additional 17 days.
Interest for 17 days = (2% / 365) * $699 * 17
Total interest = Interest for 90 days + Interest for remaining days + Interest for 17 days
The cost of paying off the loan 17 days later would be the total interest.
To calculate the annual simple interest rate for this amount, we can use the formula:
Annual interest rate = (Total interest / (Purchase price + Sales tax)) / 17 days * 365
This will give us the annual simple interest rate for paying off the loan 17 days later.
1. If Sara pays off the balance within 90 days, she will pay the purchase price ($699) plus sales tax (8.25% of $699), which is $59.67. Therefore, the total amount she will pay is $699 + $59.67 = $758.67.
2. If Sara bought the washer and dryer on December 15, her deadline for paying no interest in a non-leap year would be 90 days after December 15th. To calculate this, we need to count the days remaining in December (16 days), then count the days in January (31 days), and finally count the days in February (28 days). So in a non-leap year, her deadline would be 16 + 31 + 28 = 75 days after December 15th, which is March 1st.
In a leap year, the deadline would be 16 + 31 + 29 = 76 days after December 15th, which is February 29th.
Considering that the finance company is likely to use exact interest, they would use the exact number of days in a year, 365 (366 in a leap year), to calculate interest accurately.
3. If Sara's IRS refund does not come until April 1, her payoff amount would be the purchase price ($699) plus sales tax ($59.67) plus 26.8% annual simple interest for the first 90 days. To calculate the interest for the first 90 days, we need to convert the annual interest rate to a daily rate by dividing it by the number of days in a year (365 in a non-leap year).
Interest for the first 90 days = (26.8/100) * $699 * (90/365) = $45.46
Therefore, her payoff amount would be $699 + $59.67 + $45.46 = $804.13.
4. If Sara paid off the loan 17 days later, she would have exceeded the 90-day period. So she would need to pay the purchase price ($699) plus sales tax ($59.67) plus the interest for the first 90 days plus the interest for the remaining 17 days.
Interest for the first 90 days = (26.8/100) * $699 * (90/365) = $45.46
Interest for remaining 17 days = (2/100) * ($699 + $59.67) * (17/365) = $2.54
Total interest = $45.46 + $2.54 = $48
Total amount paid = $699 + $59.67 + $48 = $806.67
To find the annual simple interest rate, we can use the formula: Interest = Principal * Rate * Time
$48 = $699 * Rate * (107/365)
Rate = $48 / ($699 * 107/365)
Rate = 10.20%
So the annual simple interest rate for paying off the loan 17 days later is approximately 10.20%.