The question you opened
Zero percent, or 10 percent off for cash
A 1,200 dollar sofa: 0 percent over 12 months, or 10 percent off for paying today.
How much does the 0 percent deal cost you, in dollars?
$120
The plan gives up a 120 dollar cash discount. That 120 is the interest.
The real question is what the sofa costs under each choice. Paying cash costs 1,080. Taking the plan costs 1,200 spread over a year. The difference is 120 dollars, and that is what borrowing costs, whatever the sign says. Expressed as a rate it is worse than it looks. You are borrowing 1,080, the cash price, and paying back 1,200 in twelve instalments.
Since the balance falls each month, the average amount owed over the year is roughly half of it, so the effective annual rate lands somewhere near 20 percent. Comparing 120 to 1,080 and calling it 11 percent understates the cost, because you do not have the full sum for the full year. This is why finance offers and cash discounts are almost never available together.
The retailer funds the interest free plan out of margin, and the cash discount is that same margin handed back. Only one of them can be paid out. The general rule for any zero percent offer is to find the price for someone who does not take it. If a cash buyer pays the same, the finance really is free and worth taking, since money later is worth less than money now.
If a cash buyer pays less, the gap is the interest, and it should be compared with what the same money would cost from a bank. A last point that is easy to miss. Zero percent deals usually carry a penalty rate if a payment is late, often applied retroactively to the whole balance. The headline rate describes the good case, and the terms describe the other one.
Technique: Compare against the cash price