One financial institution is offering a 1% interest rate on savings accounts while another institution is offering a 2% interest rate on savings accounts. Out of the two financial institutions, which offer would the bank probably be offering

1%

Explanation:

One of the way through which banks make profit is by investing in some other financial institutions. The interest on this type of deposit forms a major component of the banks' profit .

We also need to know that the money invested by banks are the deposit made by the banks customers , who in return is also  expecting a certain amount as interest on his deposit.

Based on this explanation , a bank will offer a lower interest rate compared to the financial institution's interest in order to make its share of the of profit on its customers money invested in other financial institution.