Bank capital performs several important roles except:

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To approach this question, let's examine what bank capital is generally credited with doing and which roles it is not primarily associated with.
Option a: providing some protections to the depositors in case of liquidation. This is a core function of bank capital. Adequate capital acts as a cushion to absorb losses and protects depositors by strengthening the bank's solvency during distress, making this statement true about capital.
Option b: increasing the bank's interest rate margin. This is not a direct or primary role of bank capital. The interest rate margin is more closely tied to a bank's pricing strategy, risk premium, funding costs, asset mix, and competition. Capital quality or quantity does not inherently set or widen the margin; capital primarily supports solvency and regulatory requirements rather than deterministically widening margins. Thus, this option describes a function that is not typically associated with bank capital.
Option c: helping to maintain public confidence and avoid bank runs in case of loan borrowers default. This is another fundamental role of capital. A well-capitalized bank can absorb losses and continue to meet obligations, which sustains public confidence and reduces the likelihood of runs when borrowers default, so this option is true.
Option d: serving as a source of funds for expansion. Bank capital serves as internal funds that support growth and expansion activities, often used to fund lending growth and regulatory capital requirements, so this option is also true.
In summary, the statement that stands apart as not being a primary role of bank capital is the idea that capital increases the bank's interest rate margin. The other choices describe established protections, confidence-building effects, and growth uses that capital enables, whereas margin expansion is more a function of pricing decisions and funding costs rather than capital adequacy itself.

Bank capital performs several important roles except:

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