Two customers took out automobile loans. Katy took out a 5-year loan for $18,000 and paid 7.00% annual simple interest. Frank took out a 6-year loan for $18,000 and paid 6.00% annual simple interest. What is the difference between the amounts of interest Katy and Frank paid for their loans?

The difference between the amounts of interest Katy and Frank paid for their loans is $180

Step-by-step explanation:

The formula of the simple interest is I = Prt, where

P is the amount of the loan r is the interest rate in decimal t is the time

Katy took out a 5-year loan for $18,000 and paid 7.00% annual simple interest

∵ The amount of her loan is $18,000

∴ P = 18,000

∵ The annual simple interest is 7%

∴ r = 7% = 7 : 100 = 0.07

∵ The loan is for 5 years

∴ t = 5

- Substitute these values in the formula above

∴ I = 18,000 (0.07) (5)

∴ I = 6,300

∴ Katy will pay $6,300 interest for her loan

Frank took out a 6-year loan for $18,000 and paid 6.00% annual simple interest

∵ The amount of his loan is $18,000

∴ P = 18,000

∵ The annual simple interest is 6%

∴ r = 6% = 6 : 100 = 0.06

∵ The loan is for 6 years

∴ t = 6

- Substitute these values in the formula above

∴ I = 18,000 (0.06) (6)

∴ I = 6,480

∴ Frank will pay $6,480 interest for his loan

∵ The difference between their interests = 6,480 - 6,300

∴ The difference between their interests = $180

The difference between the amounts of interest Katy and Frank paid for their loans is $180

180

Step-by-step explanation:Apply the formula I = Prt, where I is interest, P is principle, r is rate, and t is time.

I = 18,000 (

7

100

) (5) = 18,000 (0.07) (5) = 6,300

I = 18,000 (

6

100

) (6) = 18,000 (0.06) (6) = 6,480

Therefore, 6,480 - 6,300 = 180