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?
To answer these questions, we need to break down the financing terms and calculate the payments at different points in time. Let's go step by step:
1. If Sara pays off the balance within 90 days, she will pay the purchase price plus sales tax. The total cost of the washer and dryer is $699 + 8.25% sales tax.
Sales tax = $699 * 0.0825 = $57.67
Total cost with tax = $699 + $57.67 = $756.67
Therefore, if Sara pays off the balance within 90 days, she will pay $756.67.
2. To determine the deadline for paying no interest, we need to consider the exact interest calculation. In a non-leap year, Sara bought the washer and dryer on December 15. Therefore, she has until March 15 (90 days) to avoid paying any interest.
In a leap year, we need to account for the additional day in February. So, the deadline for paying no interest would be March 16.
The finance company is likely to use exact interest because it is more accurate and fair to both the lender and the borrower. It ensures that interest is only charged for the exact number of days the loan is outstanding.
3. If Sara's IRS refund does not come until April 1, and we assume ordinary interest for a non-leap year, we need to calculate the payoff amount, including interest.
The purchase price plus sales tax is $756.67 (as calculated in question 1).
From December 15 to March 15 is a total of 90 days, which is the interest-free period. So, Sara does not have to pay any interest for this period.
From March 16 to April 1, which is 16 days, we need to calculate the interest at the rate of 26.8% annually (for the first 90 days) and 2% per month thereafter.
Interest from March 16 to April 1 = ($756.67 * 26.8% / 365) * 16 (number of days) = $3.70
Payoff amount = $756.67 + $3.70 = $760.37
Therefore, if Sara's IRS refund does not come until April 1, her payoff amount would be $760.37.
4. To calculate how much it cost Sara to pay off the loan 17 days later, we need to consider the additional interest accrued beyond the 90-day interest-free period.
From December 15 to March 15 is 90 days, which is the interest-free period.
From March 16 to March 31 is 17 days, for which we need to calculate the interest at 2% per month on the unpaid balance.
Interest from March 16 to March 31 = ($756.67 * 2% / 365) * 17 (number of days) = $0.16
Payoff amount = $756.67 + $0.16 = $756.83
Therefore, it cost Sara an additional $0.16 to pay off the loan 17 days later.
To calculate the annual simple interest rate, we can use the formula:
Interest rate = (Interest / Principal) * (365 / Number of Days)
Interest rate = ($0.16 / $756.67) * (365 / 17) = 4.43%
Therefore, paying off the loan 17 days later amounted to an annual simple interest rate of 4.43%.
Please note that all calculations are based on the provided information and assumptions. It's always advisable to verify the terms and conditions with the finance company for accurate calculations.