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To calculate the effective rate on a discounted basis with compensating balance, it is important to understand the relationship between stated interest rates, the impact of compensating balances, and how these factors modify the overall cost of borrowing.

The correct formula accounts for the stated interest rate adjusted by the presence of a compensating balance. A compensating balance is a minimum balance that must be maintained in a bank account, which reduces the usable funds available to the borrower. In other words, the borrower is effectively paying interest on a larger amount of principal than they actually get to use.

To derive the effective rate, it is essential to start by recognizing that the available funds are less than the total funds due to the compensating balance. The formula provided calculates the stated rate in proportion to the net funds available after accounting for the compensating balance deductions.

In this case, by subtracting the compensating balance percentage from 1.0, we reflect the portion of the loan that is being utilized by the borrower. Thus, the stated rate is divided by this modified figure, providing a true measure of the effective cost of borrowing when considering the restrictions imposed by the compensating balance. This effectively adjusts the nominal rate to reflect a higher cost of funds.

Therefore, the