How this instrument works
Cash back is a rebate, not a yield. An issuer returns a fixed fraction of every dollar routed through its card, so reward = spend × rate ⁄ 100 — one multiplication, no compounding, and no time anywhere in it. Double what goes through and you exactly double what comes back; the line through the origin never bends. That flatness is precisely what separates a rebate from interest, where elapsed time is the whole story.
An annual charge is what bends the picture. Subtracting it gives net = spend × rate ⁄ 100 − fee, a straight line that begins below zero and crosses only once enough has been spent. Set net to zero and the crossing falls out on its own: breakeven spend = 100 × fee ⁄ rate. A $95 charge against a 2% rate wants $4,750 of qualifying spend before the plastic has covered its own keep, after which each dollar clears two cents.
One rate on this sheet stands in for a card that probably pays several. Bonus tiers nearly always carry a ceiling — 5% on a first $1,500 of quarterly groceries stops at $75, then reverts to 1% — so the honest number to type is a blended rate: last year's total rebate divided by last year's total spend, times 100. Rebates are also computed on what was charged, which includes sales tax, and they ignore whatever interest may be accruing underneath.
- Put a year of card spending — or a single purchase — into Amount spent, $.
- Set Cash-back rate, % to the rate that genuinely applies: a headline figure for a flat card, a blended figure for a tiered one.
- Type the yearly charge into Annual card fee, $, or leave it at zero for a card that charges nothing to hold.
- Read Cash back earned for the gross rebate, then Net benefit after fee for what remains once that charge is paid.
- Raise Amount spent, $ until Net benefit after fee crosses zero — that spend is where a fee-charging card starts paying.
Worked example — $2,000 on a flat 1.5% card
Suppose $2,000 went across a flat 1.5% card last quarter and nothing is charged to hold it. Enter 2000 into Amount spent, $, 1.5 into Cash-back rate, % and 0 into Annual card fee, $. The rebate is 2000 × 1.5 ⁄ 100 = $30 exactly, and with nothing to subtract, Net benefit after fee reads $30 too.
Thirty dollars is the entire result, which is useful for gauging its scale. One month of revolving that same $2,000 at a 22% purchase rate costs about $36.67 in finance charges — more than a whole quarter of rebate. This sheet is exact about the rebate and silent about that charge, because no field here carries a balance.
Now hand the same card a $95 yearly charge and hold 1.5%. Net benefit after fee turns to −$65 on $2,000 of spend, and reaches zero only at 100 × 95 ⁄ 1.5 = $6,333 of qualifying spend a year. Below that, holding costs more than earning returns; above it, each further dollar clears 1.5 cents.
Questions
Does this include interest on a balance I carry?
No, and that omission matters more than any other. Rebates run at roughly 1% to 2% a year of spending; purchase finance charges run at roughly 20% a year of whatever balance remains unpaid. A single revolving month can erase several months of earning. This sheet has no balance field and no rate of charge, so treat its output as the rebate alone, never as a summary of what a card did to your money.
My card pays 5% in some categories and 1% elsewhere — which rate do I type?
Type a blended rate, not the headline. Add up every rebate posted over twelve months, divide by every dollar of spend across the same twelve months, and multiply by 100. A card advertised at 5% often blends out near 1.6% once the quarterly ceiling and the ordinary-purchase floor are both counted. Feeding the headline figure into a single-rate model overstates the year by a wide margin.
Why is my statement smaller than the figure shown here?
Several exclusions live between total charges and qualifying spend. Balance transfers, cash advances, gambling and money-order purchases, fees, interest and returned items usually earn nothing. Bonus categories are keyed to merchant category codes, so a supermarket counter inside a warehouse club can code as general retail and pay a base rate. Refunds also claw back rebate already posted. Subtract those from Amount spent, $ before comparing.
How much spend does an annual fee need before it pays off?
Divide the fee by the rate and multiply by 100: breakeven spend = 100 × fee ⁄ rate. A $95 fee at 2% needs $4,750 a year; the same fee at 1.5% needs $6,333. That figure only counts rebate — statement credits, lounge access or insurance attached to a card sit outside this arithmetic entirely, so a fee card can land above or below its breakeven depending on things no formula here measures.
Is a rebate treated as taxable income?
Rebates earned by spending are generally treated as a reduction in what you paid rather than as income, which is why issuers do not usually report them. Rewards handed over without any purchase requirement can be treated differently. Rules turn on specifics, so read IRS Publication 525 or ask a tax professional about your own situation. Nothing on this sheet models tax of any kind.
Is 2% back the same thing as 2% off?
Close, but not identical, and the gap has two parts. A discount comes off at the till and in most places shrinks the sales-tax base along with the price; a rebate is computed on the full amount charged, tax included, so it lands on a slightly larger base. Timing differs too — money off is immediate, whereas a rebate posts weeks later and is worth marginally less for having waited.
References
- CFPB — Credit cards: consumer tools and card agreements
- Federal Reserve — G.19 Consumer Credit release
- IRS Publication 525 — Taxable and Nontaxable Income
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.