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?
2. Find the month payemt on a water bed if the installment price is $ 1,050, the down payment is $200, and there are 10 monthly payments.
4. Find the refund fraction for a 60-month loan if it is paid in full with 22 months remaining.
1. If Sara pays off the balance within 90 days, she will pay the purchase price of $699 plus the sales tax of 8.25%.
Sales tax = $699 * 0.0825 = $57.68
Total payment = $699 + $57.68 = $756.68
2. If Sara bought the washer and dryer on December 15, using the exact interest, her deadline for paying no interest would be March 15 in a non-leap year and March 16 in a leap year. The finance company is likely to use exact interest because it is a more accurate method of calculating interest.
3. If Sara's IRS refund does not come until April 1, her payoff amount would include the purchase price, sales tax, and the accumulated interest. Since it is assumed to be a non-leap year and ordinary interest is used, the interest rate is 26.8% for the first 90 days and 2% per month after 90 days.
First, calculate the interest for the first 90 days:
Interest for 90 days = $699 * 0.268 = $187.33
Next, calculate the interest for the remaining days (between December 15 and April 1):
Number of days between December 15 and April 1 = 108 days
Number of months after 90 days = (108 - 90) / 30 = 0.6 months (rounding up to the nearest month)
Interest for the remaining days = $699 * 0.02 * 0.6 = $8.38
Total interest = Interest for 90 days + Interest for remaining days = $187.33 + $8.38 = $195.71
Payoff amount = Purchase price + Sales tax + Total interest = $699 + $57.68 + $195.71 = $952.39
4. If Sara paid off the loan 17 days later, she would have to pay interest for those additional 17 days. The annual interest rate is assumed to be the same as before, which is 26.8% for the first 90 days and 2% per month after 90 days.
First, calculate the interest for the additional 17 days:
Interest for 17 days = $699 * 0.268 * 17 / 90 = $33.28
Total amount paid = Purchase price + Sales tax + Total interest (including the additional 17 days)
= $699 + $57.68 + $195.71 + $33.28 = $985.67
To calculate the annual simple interest rate, we can use the formula:
Interest = Principal * Rate * Time
Rearranging the formula, we get:
Rate = Interest / (Principal * Time)
Using the values from the previous calculations,
Rate = $195.71 / ($699 * 90/365) = 0.1169 = 11.69%
2. To find the monthly payment on a water bed, we subtract the down payment from the installment price and then divide it by the number of monthly payments.
Installment price = $1,050
Down payment = $200
Number of monthly payments = 10
Monthly payment = (Installment price - Down payment) / Number of monthly payments
= ($1,050 - $200) / 10 = $85
Therefore, the monthly payment on the water bed is $85.
4. To find the refund fraction for a 60-month loan with 22 months remaining, divide the number of remaining months by the total number of months.
Number of remaining months = 22
Total number of months = 60
Refund fraction = Number of remaining months / Total number of months
= 22 / 60 = 0.3667 = 36.67%
1. To calculate the amount Sara would pay if she pays off the balance within 90 days, we need to add the purchase price and the sales tax.
Purchase price: $699
Sales tax (8.25%): $699 * 0.0825 = $57.67
Total amount to be paid within 90 days: $699 + $57.67 = $756.67
2. To determine Sara's deadline for paying no interest, we need to calculate the 90-day period from the purchase date.
In a non-leap year, there are 365 days. So, if Sara bought the washer and dryer on December 15, her deadline for paying no interest would be March 15 (December 15 + 90 days).
In a leap year, there are 366 days. So, if it's a leap year, her deadline for paying no interest would be March 16 (December 15 + 90 days), as there is one extra day in the year.
The finance company is likely to use exact interest because it is more precise for calculating interest on a daily basis.
3. If Sara's IRS refund does not come until April 1, she would need to pay off the balance including the interest for the extended period.
To calculate the interest, we first need to determine the number of days from the purchase date (December 15) to April 1.
December 15 to December 31: 17 days
January 1 to March 15: 74 days
March 16 to April 1: 17 days
Total number of days: 17 + 74 + 17 = 108 days
Then we can calculate the interest using the annual simple interest rate. Given that it's a non-leap year, the daily interest rate would be 26.8% / 365 = 0.073424658%
Interest for the extended period: $756.67 * 0.073424658% * 108 = $5.88
Total payoff amount: $756.67 + $5.88 = $762.55
4. To determine how much it cost Sara to pay off the loan 17 days later, we need to calculate the interest for the additional 17 days.
Given that there are 365 days in a non-leap year, the daily interest rate remains 26.8% / 365 = 0.073424658%
Interest for the additional 17 days: $756.67 * 0.073424658% * 17 = $0.86
Total payoff amount after 17 days: $756.67 + $0.86 = $757.53
To calculate the annual simple interest rate, we can use the formula:
Interest rate = (Interest / Principal) * (365 / Days)
Days = 365
Principal = $756.67
Interest = $0.86
Interest rate = ($0.86 / $756.67) * (365 / 17) = 0.0637 or 6.37%
2. To find the monthly payment on a water bed with an installment price of $1,050 and a down payment of $200, we need to subtract the down payment from the installment price to get the total balance to be paid over the 10 monthly payments.
Total balance: $1,050 - $200 = $850
Monthly payment: $850 / 10 = $85
So, the monthly payment on the water bed is $85.
4. To find the refund fraction for a 60-month loan with 22 months remaining, we need to divide the number of remaining months by the total number of months.
Refund fraction: 22 months / 60 months = 0.3667 or 36.67% (rounded to two decimal places)
Therefore, the refund fraction for the 60-month loan is approximately 36.67%.