The formula
extra cost = payments + deposit − cash price · the real rate is the IRR of that schedule
Where it comes from
Paying 10% more over a year is not a 10% interest rate, because you do not owe the full amount for the whole year. As you pay it down, the balance shrinks, so the same extra cost is being charged on progressively less money. That is what pushes the real rate to nearly twice the headline figure.
How to work it out by hand
- Add up all the payments, plus any deposit
- Subtract the cash price: that is the extra cost
- Find the rate that makes the payment schedule equal the cash price
- Compare it against what your money earns if you keep it
What is worth knowing
The doubling is the point worth remembering: a surcharge of X% spread over monthly instalments works out at roughly 2X% a year, because the average balance outstanding is about half the original. It is the reason interest-free finance and instalment plans are compared on the wrong number so often. Genuine 0% finance is a different case and usually worth taking, since keeping your cash earns something and costs nothing — but check whether the cash price is discounted, because a “0% finance or 10% off for cash” offer is a 10% interest charge wearing a disguise.