Zero per cent finance is rarely free when a cash price is on offer. Turn the lost discount into an interest rate and compare it with what your money earns or a loan costs.
Zero per cent finance costs whatever discount you give up by taking it. On a £12,000 purchase with £1,000 off for cash, choosing 36 payments of £333.33 instead is borrowing £11,000 at an implied 5.89 per cent APR. That is cheaper than an illustrative 7.9 per cent personal loan, but dearer than leaving the cash in savings at 4.5 per cent, where paying cash comes out £220.84 ahead in today's money.
Worked in full in Personal Finance for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Cars, furniture, kitchens and phones are often sold with a choice: a lower price if you pay now, or the full price spread over months at 0 per cent. The finance is advertised as free and, measured on the full price, it is. Measured on the price you could have paid, it is a loan whose interest has been moved into the sticker. The question is never "is 0 per cent good?" but "what rate am I really paying, and what does my money earn instead?"
| Item | Value |
|---|---|
| Full price | £12,000 |
| Finance: 0% over 36 months | £333.33 a month |
| Cash price, with discount | £11,000 |
| Discount given up by financing | £1,000 |
| Alternative 1: savings account, AER | 4.5% |
| Alternative 2: personal loan, APR | 7.9% |
Find r such that payment × (1 − (1 + r)−n) / r = cash price
£333.33 × 36 payments has a present value of £11,000 at r = 0.4781 per cent a month. As an annual rate: 5.74 per cent nominal, and an APR of 5.89 per cent once monthly compounding is included.
In a spreadsheet: =RATE(36, -333.33, 11000) gives the monthly rate; =(1+RATE(36, -333.33, 11000))^12-1 gives the APR.
The seller is lending you £11,000 and taking back £12,000. The extra £1,000 is interest, collected as a higher price. The difference between the 5.74 and the 5.89 per cent is the same one that separates a quoted rate from its annual equivalent, explained in APR vs APY.
If you have the cash in savings. Paying £11,000 now gives up interest. Keeping the £12,000 in a 4.5 per cent account and paying £333.33 out of it each month would earn £889.15 over the three years, worth £779.16 in today's money: less than the £1,000 discount. In today's money the 36 payments are worth £11,220.84 at the savings rate, so paying cash saves £220.84. Cash wins.
If you would have to borrow the cash. A 7.9 per cent APR loan for £11,000 over 36 months costs £342.81 a month, £12,341.28 in all. The 0% plan costs £333.33 a month, £12,000.00 in all: £341.28 less. Finance wins, because the seller's 5.89 per cent is cheaper than the bank's 7.9. The payment arithmetic for the loan is set out in how a loan's monthly payment is calculated.
| Route | Monthly | Total paid | Effective rate |
|---|---|---|---|
| Pay cash from savings | 0 | £11,000 | gives up 4.5% |
| 0% finance | £333.33 | £12,000.00 | 5.89% |
| Personal loan, pay cash | £342.81 | £12,341.28 | 7.9% |
| Discount for cash | As % of price | Implied APR over 36 months |
|---|---|---|
| £250 | 2.1% | 1.38% |
| £500 | 4.2% | 2.82% |
| £1,000 | 8.3% | 5.89% |
| £1,500 | 12.5% | 9.26% |
| £2,000 | 16.7% | 12.96% |
Against savings at 4.5 per cent, the break-even discount is £779.16, 6.5 per cent of the price: below it take the finance and keep the cash earning; above it, pay cash. Against a 7.9 per cent loan the break-even is £1,304.19, 10.9 per cent. The length of the plan matters as much: the same £1,000 discount implies 4.42 per cent over 48 months, 8.84 per cent over 24 and 17.66 per cent over 12, because the same £1,000 of hidden interest is charged on money borrowed for less time.
The comparison also has a side the arithmetic cannot see. A finance agreement is a credit application: it usually involves a credit search and adds a monthly commitment that lenders will count when you next apply for a mortgage or a loan. Paying cash keeps that capacity free. If a large purchase is planned in the next year or two, that is a reason to lean towards cash even when the numbers are close.
Turn the discount into a rate: here 5.89 per cent. Pay cash if your savings earn less than that; take the finance if your alternative is borrowing at more. On these figures cash from savings wins by £220.84 and the 0% plan beats a loan by £341.28. Personal Finance for Beginners lists the questions to ask before signing any debt offer, and the free working documents for the book include them on one printable page.
Find the rate at which the instalments are worth the cash price. Thirty-six payments of £333.33 have a present value of £11,000 at 0.4781 per cent a month, an APR of 5.89 per cent. In a spreadsheet: =RATE(36, -333.33, 11000), then (1 + result)^12 minus 1. With no discount for cash the rate really is zero.
Any discount larger than the interest your cash would earn while you paid by instalments. With savings at an illustrative 4.5 per cent, a discount above £779.16, 6.5 per cent of a £12,000 price over 36 months, makes cash cheaper. If you would have to borrow the cash at 7.9 per cent, the discount must exceed £1,304.19 before borrowing to pay cash beats the 0% offer.
Yes, sharply. The same £1,000 of hidden interest is charged on money borrowed for less time. Over 48 months the implied rate is 4.42 per cent, over 24 months 8.84 per cent and over 12 months 17.66 per cent. A large discount against a short 0% plan is an expensive loan dressed as a free one.
This article is one calculation from Personal Finance for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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