A. lender
Let's look at the options and see what makes sense.
A. lender
* A lender is someone who loans money to another party and expects to get that money back in the future plus some interest in addition to the original amount loaned. This pretty much describes the situation between the customer and the bank in this problem, so this is the correct choice.
B. investor
* An investor provides money to another party and hopes to get back more money than originally provided, but accepts the risk that the investment may fail and not return a profit. An investment is fairly high risk, but with that risk has the possibility of a high return. This doesn't describe the situation with the bank, so this is a bad choice.
C. insurer
* An insurer will for a sum provide compensation if an adverse event happens. Banks in America are insured with the FDIC so that if they become insolvent, the deposits the bank was holding will be repaid to the depositors up to the insured limit. This doesn't describe the situation in the question, so this is also a bad choice.
D. borrower
* A borrower borrows money for immediate use with the intention of paying back that loan in the future along with some interest. This doesn't describe the situation in the problem, so it's also a bad choice.