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I started listing revenue sources fine (interchange, interest income) but fumbled on the cost side.
First, outline the revenue and cost components of a credit card issuer, then set up a break-even equation where the incremental cashback cost is offset by additional interest income from higher balances. Solve for the required average balance by equating the cashback rate (as a percentage of spend) to the interest rate times the balance difference.
Pro tip: Clarify that the break-even balance depends on the cashback rate and the interest rate; without those, express the answer as a formula. If the cashback rate is, say, 2% and interest rate is 20%, the required balance is $1,000 + (0.02 * spend) / 0.20, but if spend is not given, assume it's proportional to balance or state the assumption.
List key revenue sources: interest income, interchange fees, annual fees, and other fees. List key costs: rewards (cashback), fraud losses, operational costs, marketing, and cost of funds.
For the no-cashback card, profit = interest income + interchange - costs. For the cashback card, profit = interest income + interchange - cashback - costs. Assume other costs are equal.
Equate the incremental interest income from the cashback card's higher balance to the cashback cost. Let r be interest rate, c be cashback rate, S be spend, and B be the additional balance needed. Then r * B = c * S.
If spend S is not given, assume it is proportional to balance or express B in terms of S. If S is assumed equal to the no-cashback balance ($1,000), then B = (c * 1000) / r, and total balance = 1000 + B.
Highlight that the result depends on the cashback rate, interest rate, and spend-to-balance ratio. Mention that in reality, cashback users may spend more, which increases interchange revenue and changes the break-even point.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.