Cashback Against Interest: The Payoff Fraction Below Which a Rewards Card Costs More Than It Returns

A cashback card paying 1.5% is routinely described as 'free money' for spending the household would do anyway. That description holds only for balances paid in full. This paper simulates a household spending USD 1,400 a month on such a card at 24.9% APR, paying a fixed fraction of each statement in full and revolving the rest, and finds the break-even fraction: below paying 59% of the balance each month, the interest on the revolving balance exceeds the cashback, which is USD 21.00 a month. At a 90% payoff fraction the household already carries a steady balance of USD 159.15 and loses money net; at 80% the net loss is USD 13.70 a month with sign reversed — that is, interest exceeds cashback by that amount. A single month's spending carried for three months costs USD 88.97 in interest, wiping out 4.2 months of cashback. The study is simulated, not measured. SIMULATED, NOT MEASURED.