What are the specific, agreed terms in the rental agreement?
There are likely terms permitting the consumer or the business to terminate the rental agreement, and then specify how continued debt is then to be handled.
For example, does the agreement permit you to terminate the rental upon notice, either based on your decision to return the instrument, or, if lost, to separately pay for the lost instrument? I would presume that notice of termination of the rental would be separate from the issue of any obligation to return the instrument, or to pay for it should you not return it.
It would seem that you could not terminate the rental and yet keep the instrument, which would effectively permit your continued rental at no rental fee.
What are the provisions of your agreement regarding both termination of rental, and return of the equipment?
I assume since it's a rental the 19 a month is the fee.. Somehow the terms state that it goes up. Did you contact them about the lost instrument? Might seem better to pay them off over 19 every month.
Did you ever report the instrument lost to the rental company? If yes, did the rental company charge you a replacement fee? If yes, did you pay this fee. If no to the first question, you may wish to contact the rental company and work out something.