County Bank offers one$-$year loans with of $9$ per cent stated or base rate but requires a compensating balance of $10$ per cent. What is the true cost of this loan to the borrower? How does the cost change if the compensating balance is $15$ per cent? If the compensating balance is $20$ per cent? $[$Hint: true cost $=$ loan rate $-$: $(1$ compensating balance rate$)]$