They are possible, and they are done in this forum, on the Lending section
Through the blockchain it isn't possible... And I don't really see that as a useful addition to Bitcoin, honestly
Yes, I meant on the blockchain.
So, a script couldn't schedule new transactions to repay the principal + interest?
If you can't see:
Bitcoin is a currency. Loan is not and must never be a feature of a currency.
Friend, this is a currency not some sort of lending place. Please do understand... Have you ever found a currency with loan as it's feature like what you are saying now? No! There will be additional places to conduct this lending business or you can open one for yourself.
The main drawback of your request is that blockchain can't force users to *fund* repayment address.