When does he have to pay me back and is the paper he wrote binding since I did not sign it?

You loaned him money based on his agreement to repay you.  There is no need for a written contract, an oral contract will do.  However, in situations where a writing is required, it would generally (unless it expressly provides otherwise) only have to be signed by the party against whom it is being enforced, here the borrower.  To the extent that any court deems the time of repayment to be ambiguous, which I doubt, it is nevertheless likely to conclude that the borrower is required to pay when he gets his next tax refund (I assume you meant refund, not return).  If the contract had not set forth any time for repayment, the court would imply a reasonable time under the circumstances; it is very doubtfal that any court would hold that the borrower had years to pay under these circumstances, unless he has some strong evidence that this was agreed to.