Ella is buying a motorcycle and is taking out a loan in the amount of $15,000. Her choices for the loan are a 36-month loan at 6.50% annual simple interest and a 48-month loan at 7.50% annual simple interest. What is the difference in the amount of interest Ella would have to pay for these two loans?
Responses
A $1,025$1,025
B $1,275$1,275
C $1,575$1,575
D $2,925
To find the difference in the amount of interest paid for the two loans, we need to calculate the interest for each loan separately.
For the 36-month loan at 6.50% annual simple interest, the total interest paid would be:
$15,000 * 0.065 = $975 per year
$975 * 3 years = $2,925
For the 48-month loan at 7.50% annual simple interest, the total interest paid would be:
$15,000 * 0.075 = $1,125 per year
$1,125 * 4 years = $4,500
The difference in the amount of interest paid would be:
$4,500 - $2,925 = $1,575
Therefore, the answer is C) $1,575
To find the difference in the amount of interest Ella would have to pay for these two loans, we need to calculate the interest for each loan and then subtract the interest for the 36-month loan from the interest for the 48-month loan.
For the 36-month loan, the interest can be calculated using the formula:
Interest = Principal * Rate * Time
Interest = $15,000 * 6.50% * (36/12) = $3,250
For the 48-month loan, the interest can be calculated using the same formula:
Interest = $15,000 * 7.50% * (48/12) = $4,500
Now, let's find the difference in the amount of interest:
Difference = Interest for 48-month loan - Interest for 36-month loan
Difference = $4,500 - $3,250 = $1,250
Therefore, the correct answer is option B: $1,275.
To find the difference in the amount of interest Ella would have to pay for these two loans, we need to calculate the interest for each loan.
For the 36-month loan at 6.50% annual simple interest:
First, we calculate the interest for one year:
Interest = Principal * Rate = $15,000 * 6.50% = $975
Since the loan duration is 36 months, we multiply the interest for one year by 3 to get the total interest:
Total Interest = $975 * 3 = $2,925
For the 48-month loan at 7.50% annual simple interest:
First, we calculate the interest for one year:
Interest = Principal * Rate = $15,000 * 7.50% = $1,125
Since the loan duration is 48 months, we multiply the interest for one year by 4 to get the total interest:
Total Interest = $1,125 * 4 = $4,500
Now, to find the difference in the amount of interest, we subtract the total interest of the 36-month loan from the total interest of the 48-month loan:
Difference = $4,500 - $2,925 = $1,575
Therefore, the difference in the amount of interest Ella would have to pay for these two loans is $1,575.
The correct answer is C. $1,575.