The correct answer is A. He assured her that he would repay her loan.
The sentence “Rest assured. I shall repay your loan” is an assurance. It means that the speaker is confident that he will be able to repay the loan. The other options are not as accurate. Option B, “He told her that he would repay her loan,” is a more general statement. It does not convey the speaker’s confidence in his ability to repay the loan. Option C, “He said that he might repay her loan,” is a less confident statement. It suggests that the speaker is not sure if he will be able to repay the loan. Option D, “He told her not to worry about the repayment of her loan,” is a different type of statement. It does not directly address the issue of whether or not the speaker will repay the loan. Instead, it tells the listener not to worry about it.