Janet Foster bought a computer and printer at Computerland. The printer had a $620 list price with a $100 trade discount and 2/10, n/30 terms. The computer had a $2,200 list price with a 25% trade discount but no cash discount. On the computer, Computerland offered Janet the choice of (1) paying $90 per month for 17 months with the 18th payment paying the remainder of the balance or (2) paying 8% interest for 18 months in equal payments.
a. Assume Janet could borrow the money for the printer at 8% to take advantage of the cash discount. How much would Janet save? (Use 360 days a year. Round your answer to the nearest cent.)
Janet's savings
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To calculate Janet's savings by borrowing the money for the printer at 8% interest, we need to find the amount of the cash discount and compare it to the interest paid.
The list price of the printer is $620, and there is a $100 trade discount. So, the selling price of the printer can be calculated as follows:
Selling Price of Printer = List Price - Trade Discount
= $620 - $100
= $520
Now, we need to find the cash discount. The terms state that there is a 2% cash discount if payment is made within 10 days. Therefore, the cash discount can be calculated as follows:
Cash Discount = Selling Price of Printer * Cash Discount Rate
= $520 * 0.02
= $10.40
Next, let's find out the interest paid if Janet borrows the money at 8% interest. Since the terms are 2/10, n/30, the borrowing period for the printer would be 20 days (30 - 10).
Interest Paid = Selling Price of Printer * Interest Rate * (Borrowing Period / Number of Days in a Year)
= $520 * 0.08 * (20 / 360)
= $0.91
Finally, we can calculate Janet's savings by subtracting the interest paid from the cash discount:
Janet's Savings = Cash Discount - Interest Paid
= $10.40 - $0.91
= $9.49
Therefore, Janet would save $9.49 by borrowing the money at 8% interest to take advantage of the cash discount for the printer.
To calculate Janet's savings, we need to determine the trade discount for the printer and compare it to the interest she would pay if she borrowed the money to take advantage of the cash discount.
The trade discount for the printer is $100.
To calculate the interest Janet would pay if she borrowed the money at 8% interest for the cash discount:
Cash discount = trade discount / (1 - cash discount rate)
Cash discount rate = 2/10 = 0.2
Cash discount = $100 / (1 - 0.2) = $100 / 0.8 = $125
Interest paid = loan amount * interest rate * time
Loan amount = $620 - $125 = $495
Interest rate = 8% = 0.08
Time = 30 days
Interest paid = $495 * 0.08 * (30/360) = $3.30
Janet's savings = trade discount - interest paid = $100 - $3.30 = $96.70
Therefore, Janet would save $96.70 if she borrowed the money at 8% to take advantage of the cash discount.