Q$2)$ Suppose a Bank expects to raise $$25$ million in new deposits by offering its depositors an interest rate of $7$ percent.

Management estimates that if a bank offers a $7\mathrm{.}50$ percent interest rate, it can raise $50$ million in a new deposit money.

At $8$ percent, $$75$ million is expected to flow in$,$ while a posted deposit rate of $8\mathrm{.}5$ percent will bring in a projected $$100$

million. Finally if the bank promises an estimated $9$ percent yield, management projects that $$125$ million in new funds

will appear in the form of both new deposits and existing deposits that customers will keep in the bank to take advantage

of the higher rates offered.

Let's assume the management can invest new deposit money, at a yield of $10\%.$ This new loan yield represents marginal

revenue; the added operating revenue the bank will generate by making new loans from the new deposits.

Given these facts what deposits interest rate should the bank offer to its customers?