[R] Regression model with proportional dependent variable

[ty ty]

Hello, dear experts. I don't have much experience in building
regression models, so sorry if this is too simple and not very
interesting question.
Currently I'm working on the model that have to predict proportion of
the debt returned by the debtor in some period of time. So the
dependent variable can be any number between 0 and 1 with very high
probability of 0 (if there are no payment) and if there are some
payments it can very likely be 1 (all debt paid) although can be any
number from 0 to 1.
Not having much knowledge in this area I can't think about any
appropriate model and wasn't able to find much on the Internet. Can
anyone give me some ideas about possible models, any information
on-line and some R functions and packages that can implement it.
Thank you in advance for any help.

Ihor.