Question

Janeanne borrowed $7,500 to buy a used car. The interest rate on the loan
was 5.5%. If Janeanne repaid a total amount of $9,975, how many years
did Janeanne borrow the money for?

Answer 1

Answer:

Around 5 years

Unless I did my work incorrectly, Janeanne borrowed for a little longer than 5 years but a LOT less than 6 years. Overall, she was closer to 5 years than she was 6 years.

Step-by-step explanation:

Presumably, each year, her interest rate went up along with her new total loan amount (thanks to the interest).

Initially: She owed $7,500

1st year: Since her interest rate is 5.5%, we have to find 5.5% of the original loan amount ($7,500) which is $412.50. Now we add that 5.5% onto the original loan.

$7,500 + 412.50 = 7,912.50$

2nd year: Now that she owes $7912.50, we need to find 5.5% of THAT loan amount, which is $435.19. Now we add again.

$7,912.50 + 435.19 = 8,347.69$

3rd year: We're at three years now and Janeanne owes around $8347.69. We once again find 5.5% of THIS amount of money. 5.5% is $459.12

.

$8,347.69 + 459.12 = 8,806.81$

4th year: At the 4 year mark, Janeanne owes $8806.81. 5.5% of that is $484.37. The total sum of these is:

$8,806.81 + 484.37 = 9,291.18$

5th year: At 5 years, Janeanne owes $9291.18. 5.5% is 511.01. Let's add them together:

$9,291.18 + 511.01 = 9,802.19$

6th year: Now at 6 YEARS, Janeanne owes $9802.19. 5.5% of this loan amount is $539.12. Added together, they equal:

$9,802.19 + 539.12 = 10,341.31$

Janeanne borrowed the money for little over 5 years. :)