Have I committed a sin by taking out an interest-bearing loan for my studies, with the intention of repaying it through a charity, and will I not be rewarded for my studies, and how can I expiate this sin?

Usurious loans are not permissible except in cases of dire necessity. If there is no necessity, then repentance is obligatory, which entails regretting the sin, abandoning it, and resolving not to return to it. If the loan’s interest is deducted immediately upon repayment of the principal, then it must be repaid as soon as one is able, for Allah the Almighty says: "But if you repent, you may have your principal – [thus] you do not wrong, nor are you wronged."