Card arithmetic from the start

What this is

Comparing reward rates on a single card is easy. It gets hard the moment you try to keep several cards alive at once, because a previous month requirement makes your spending compete with itself.

This page holds no list of cards. You give it the terms of the cards you already have and it does arithmetic on them. That is why there is no claim that one card is better, no invitation to sign up, and no outward link of that kind.

There are three screens. What a payment abroad really costs, how to split spending across the cards you hold, and how many cards are still worth holding.

How the payment network turns

When you pay abroad in the local currency, the card network fee goes on first, the result is converted at the applied rate, and the issuer overseas service fee goes on after that. The two fees multiply rather than add.

If the till offers to bill you in won and you accept, one more rate is added in front. The won figure still travels through the same network, so the card network fee and the issuer fee remain. The only difference between the two formulas is that added rate.

The applied rate is not the rate on the day you paid. It is the rate on the day the issuer settles the transaction. The Credit Finance Association guide puts that at 3 to 7 days. This is why a figure worked out on the day never quite matches the statement.

A previous month requirement asks one question: did last month reach the amount the card set. Fall short by anything and the whole month of rewards is gone. On top of that, each card excludes some kinds of spending from that count.

Why an AI subscription is charged as an overseas payment

Claude, ChatGPT, Gemini and Perplexity are sold by companies abroad, so the subscription is submitted as an **overseas payment**. You may be paying from a Korean app, but on the card network the merchant sits outside the country, and the multiplications described above apply in full.

It leaves your account every month, so one difference is repeated twelve times. A 22 dollar subscription is 264 dollars a year, and a one percent gap between two fee rates turns into an amount you can see once a year has passed. Put one month into the calculator above and multiply by twelve to see the size of it.

Some cards single out overseas payments or subscriptions for a better rate. Those numbers are set by the issuer and change often, so **we do not name a card or a percentage here.** Find the two fee rates and the reward rate in your own card's terms, put them in above, and we will do the arithmetic.

A domestic subscription billed in won (Netflix or YouTube Premium paid in Korean won, for instance) is not an overseas payment and none of this applies. Whether the statement also shows a foreign-currency amount is what separates the two.

The rules this calculator uses

Rewards on each card are counted like this. Each row is multiplied by its rate and cut at that row's monthly cap, the results are added, and the sum is cut again at the card's own monthly cap. If the previous month requirement is not met, the whole figure becomes zero.

The requirement counts only the spending that is not excluded on that card. Which rows are excluded differs by card, so mark them per row.

The objective is total monthly reward minus one twelfth of the annual fees. Fees are subtracted for every card held. That is why holding a card that cannot meet its requirement leaves only the fee.

It is solved in two stages. Every combination of cards that could meet its requirement is tried. With a combination fixed, the step function disappears and what remains is a capped concave problem, which a linear program solves exactly. Pushing each won to whichever slot looks best at the time is genuinely wrong once a card level cap binds.

The combinations are not endless. Any combination whose requirements add up past a month of spending is impossible and is dropped on the spot. That conservation is what makes the best number of cards finite.

Where to find the numbers

Rates, caps and requirements are in the card agreement or in the product notice inside the issuer app. Wording differs by product, so we cannot fill them in for you, and filling them in would itself amount to stating product terms.

Overseas fee rates are usually in the overseas usage notice or in the foreign settlement section of the terms. If the network share and the issuer share are listed separately, put them in the two separate fields.

The added rate can be estimated from a receipt that shows both the won figure and the foreign figure. Divide by the rate for that day and subtract one.

Open last month's statement and copy the amounts row by row and the split will match your real life. Rename the rows to whatever you call them.

Choosing how many cards

More cards means more access to good rates, but the same spending has to be spread thinner, so each card receives less and at some point one cannot clear its requirement. The peak sits where those two forces meet.

If you spend little, the peak arrives early, because the requirements add up past your spending quickly. If you spend a lot, several cards can stay alive and the peak moves later.

A card that excludes a lot of spending from its requirement is hard to keep alive. It is usually such a card that falls off the curve first, however good its headline rate looks.

The imagined row under the curve lets you try terms you do not hold yet and watch where the peak moves. We put no value in that row.

Where people get stuck

If nothing comes out, monthly spending is usually still empty. With every row blank there is nothing to split and the arithmetic never starts.

If it says no card can meet its requirement, the requirements add up past your spending. Holding fewer cards, or keeping the ones with lower requirements alive, is the answer.

If the overseas figure does not match your statement, the rate for the day you paid was probably used. Use the applied rate printed on the statement instead.

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