Interest-free instalments or a cash discount? How to work out which is better

"Interest-free instalments are always the better deal" gets repeated so often it sounds like a law. Sometimes it's true and sometimes it isn't: it depends on how much of a discount you get for paying cash and on what your money would do if you didn't spend it today. With those two numbers the calculation takes two minutes.

Why fixed instalments look free

An interest-free instalment is a fixed amount you pay later. If money loses value month after month, the sixth instalment "weighs" less than the first one, even though the number is the same. That's what makes instalments appealing: you pay the shop back with money that's worth less than what it lent you.

But that's only a gain if the money you didn't spend today does something in the meantime: if it sits in an interest-bearing account, a term deposit or a fund that pays a return. If it sits idle in a current account, it earns nothing, and then the only thing that matters is the total price.

The two numbers you need

• The price of each option. How much you pay in cash (with the discount, if there is one) and how much the instalments add up to.
• The monthly rate your money earns. The rate on your savings account or term deposit, converted to a month. If your money earns nothing, the rate is zero.

The calculation: bring each instalment to today

Divide each instalment by (1 + rate) raised to the number of months until you pay it. The first instalment, which usually lands on next month's statement, is divided once; the second, twice; and so on. The sum is what the instalments cost you in today's money, and that's the number you compare with the cash price.

An example: a TV at 600,000, in 6 interest-free instalments of 100,000, or 540,000 in cash (a 10% discount). At a monthly rate of 3%, the six instalments brought to today are worth 97,087, 94,260, 91,514, 88,849, 86,261 and 83,748: 541,719 in total.

• Cash: 540,000.
• Instalments, in today's money: 541,719.

It's practically a tie. Now change a single number:

• If your money earns 2% a month, the instalments are worth 560,143 today: cash wins, by about 20,000.
• If it earns 4%, they're worth 524,214: instalments win, by about 16,000.
• If there's no cash discount (you pay 600,000 either way), instalments win as long as your money earns anything.
• If your money earns nothing, paying 540,000 instead of 600,000 is simply 60,000 less.

The quick rule

If you don't want to do the whole calculation: compare the cash discount with what your money would earn over half the instalment period. With 6 instalments, half is 3 months; at 3% a month, that's about 9%. If the discount is bigger, pay cash. If it's smaller, take the instalments. It isn't exact, but it rarely picks the wrong side.

What the calculation doesn't tell you

Instalments being the better deal doesn't mean you can afford them. Every purchase in instalments is money from the coming months that already has a destination, and what surprises you at the end of the month isn't one purchase: it's the sum of several that each looked small at the time. Before adding another, check how much you've already committed; we explain how in how to keep your credit card instalments under control.

If the instalments do carry interest, the calculation is the same, just with the real amount of each instalment. And it's worth checking the total cost of credit (APR or its local equivalent) that the shop or bank has to disclose: that's what borrowing really costs.

Track it so it doesn't slip away

On Expenses you log the purchase once with the number of instalments and the app spreads it across the coming months: you see how much is due each month and how much you still owe in total, no spreadsheet needed. It's free and doesn't ask for card details.