Annual Simple Interest

Question

Sara is looking to purchase a washer and dryer. 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 any time 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

26.2​%

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

​$799

plus the

6.25%

sales tax. Sara knew that her tax refund from the IRS would be

​$1,100

so she bought the washer and dryer confident that she could pay off the balance within the 90 days.

How much did it cost her to pay off this loan

21

days​ late?

​$82.75

​(Round to the nearest cent as​ needed.)

What annual simple interest rate does this amount​ to?

nothing

​(Round to four decimal places as​ needed.)

Answer 1

simple interest = principal * rate (as a decimal) * time (in years)

799 + (6.25% of 799) + (26.2% simple interest for 90 days)

= 799 + (.0625 * 799) + ( 799 * 0.262 * 90/365 )

= 799 + 49.94 + 51.62

= 900.56

her interest is 0.262*90/365 = 6.46% for the first 90 days. if you simplify the notion that 90 days is almost 3 months, then she has 9 months left, paying 3% each month. (but if 90 days falls short of 3 months, she gets hosed for another partial month and another 3%.)

6.46% + (3% * 9)

= 6.46% + 27%

= 33.46% equivalent simple interest.