You get a $5,000 180-day 11% consumer loan on May 18. You make a $2,000 payment on July 18. Calculate the balance you still owe after the payment. Assume a 365-day year.

Various loans have their own rules. I don't know what your text is telling you, so I will compute this first on the basis of simple interest.

5000 for 180 days at 11% will need an interest payment of
.. I = P*r*t = 5000*0.11*(180/365) = 271.23
In this scenario, it doesn't matter when you make the payment(s), the total amount due is 5271.23. After a 2000 payment, you will still owe 3271.23.

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On the other hand, if your loan agreement says payments reduce the outstanding principal amout, then you can look at it this way.

Consider the interest due on day 61. That is
.. I = P*r*t = 5000*0.11*61/365 = 91.92
If that is paid first, then the outstanding principal after your 2000 payment is
.. 5000 +91.92 -2000 = 3091.92
You will be paying 11% for 119 days on that amount, so at maturity you will owe
.. 3091.92*(1 +0.11*119/365) = 3202.81