Nancy is the proud owner of a new car. She paid $1,500 up front and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?

Question

Mathematics

Gwendolen

13 April, 09:39

Nancy is the proud owner of a new car. She paid $1,500 up front and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?

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Talon Bullock · Answer 1

Step-by-step explanation:

In order to buy the new car, Nancy

paid $1,500 up front and took out a loan for the rest of the amount.

Let x = The amount of loan that she took.

The interest rate on the loan is 5%.

This means that she paid interest of 5/100 * x = 0.05 * x

= 0.05x

If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02,

It means that

1,500 + x + 0.05x is greater than 16,213.02

1500 + 1.05x = 16213.02

1.05x = 16,213.02 - 1500

1.05x = 114713.02

x = 114713.02/1.05

x = $109250.49524

The amount that Nancy borrowed is greater than $109250.49524