Question

Emma is taking out a loan in the amount of $25,000. Her choices for the loan are a 60-month loan at 5% annual simple interest and a 72-month loan at 6% annual simple interest. What is the difference in the amount of interest Emma would have to pay for these two loans?

Answer 1

The difference in the amount of interest Emma would have to pay for these two loans is $2,750

Step-by-step explanation:

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

• P is the initial amount of deposit/loan
• r is the annual rate in decimal
• t is the time in years

∵ Emma is taking out a loan in the amount of $25,000

∴ P = 25,000

∵ The first choice is a 60-month loan

- Each year has 12 months

∴ t = 60 ÷ 12 = 5 years

∵ The annual simple interest rate is 5%

∴ r = 5% = 5 ÷ 100 = 0.05

- Substitute these values in the formula above to find the

   interest amount in the first choice

∵ I = 25,000(0.05)(5)

∴ I = 6,250

∴ The interest of the first choice is $6,250

∵ The second choice is a 72-month loan

- Each year has 12 months

∴ t = 72 ÷ 12 = 6 years

∵ The annual simple interest rate is 6%

∴ r = 6% = 6 ÷ 100 = 0.06

- Substitute these values in the formula above to find the

   interest amount in the first choice

∵ I = 25,000(0.06)(6)

∴ I = 9,000

∴ The interest of the second choice is $9,000

∴ The difference in the amount of interest = 9,000 - 6,250

∴ The difference in the amount of interest = 2,750

The difference in the amount of interest Emma would have to pay for these two loans is $2,750

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Answer 2

Answer:

The answer is $2,750

Step-by-step explanation:

Apply the formula I = Prt, where I is interest, P is principle, r is rate, and t is time.

I = 25,000(5/100)(60/12) = 25,000(0.05)(5) = 6,250

I = 25,000(6/100)(72/12) = 25,000(0.06)(6) = 9,000

Therefore, 9,000 − 6,250 = 2,750