Everyday money

The zero percent that costs you 120 dollars

A sofa is 1,200 dollars. Take the store card and you pay nothing over twelve months at 0 percent. Pay today in cash and the shop takes 10 percent off.

The finance deal has no interest line on it anywhere, and it still costs 120 dollars. That is the cash discount you gave up to get it, and 120 is what the loan is priced at. The word interest never appears, so the price hides in the offer you turned down. Zero percent, or 10 percent off for cash is that comparison in one card.

Money questions rarely need long arithmetic. They need you to notice which number the seller left out.

Why does easy arithmetic go wrong on a receipt?

Three things get dropped, and each one changes the answer by a lot.

The unit goes missing. Two shampoo bottles, two prices, two sizes. Until you divide price by size you are comparing nothing. A 2 litre bottle at 3.60 works out at 1.80 a litre, and the 3 litre family size at 5.70 works out at 1.90. Bigger packs usually do cost less per litre, and the shelf label leans on that habit rather than on this particular pair of numbers.

The clock goes missing. A storefront lends you 100 dollars and asks for 115 back in two weeks. Fifteen dollars reads as a flat fee. It is 15 percent, and two weeks fits into a year 26 times, so the rate is 390 percent a year before any compounding. Every rate carries a clock, and a fee quoted without one is a rate in disguise. That is Fifteen dollars for two weeks.

The weights go missing. You put 120 dollars into a fund at 60 a share, then another 120 at 30 a share. The average of 60 and 30 is 45, and your actual cost is 40. The first 120 bought 2 shares and the second bought 4, so 240 dollars bought 6 shares. The cheaper price bought twice as many, and it pulls the average toward itself. Two buys, one average price is worth doing once before you read another cost basis.

How do you run the numbers at the counter?

Five habits handle almost every till, menu and payslip.

Split the number into pieces that divide cleanly. A dinner bill of 87 dollars split three ways looks awkward until you cut 87 into 60 and 27. Both divide by three without a remainder, so each person owes 20 plus 9, which is 29.

Take the tenth first, then adjust. For a 20 percent tip on 64 dollars, move the decimal point one place to get 6.40, then double it: 12.80. Doubling before you move the point gives 1.28 and leaves a 2 percent tip, so the order is the whole trick.

Turn a salary into an hour by halving the thousands. A full year of work is close to 2,000 hours. Dividing by 2,000 means dividing by a thousand and then by two, so 78,000 dollars a year is 39 dollars an hour. Dividing by 12 answers a different question and gives you the month. Seventy eight thousand, per hour is the version with the numbers filled in.

Price one part, then scale it. A wedding seats 120 guests at 85 dollars a plate, and food is about a third of the budget. The catering bill is 120 times 85, which is 10,200. Triple it and the whole event is around 30,600. What that wedding cost accepts anything close, because the point is the method rather than the last digit.

Convert every offer into one price for the same basket. Two shirts at 40 dollars each. Half off the second shirt costs 40 plus 20, so 60. A flat 25 percent off both costs 30 plus 30, so 60. Half off one item out of two is a quarter off the pair, which is why those two signs describe the same deal.

The mistakes that cost real money

Comparing headlines instead of prices. Half off, buy one get one, 25 percent off the pair. Until each one is a number of dollars for the same goods, they cannot be ranked.

Treating a fee as a fee. Anything charged for the use of money over a period is a rate. Fifteen dollars, 3 percent, two points at closing: give each one a time frame and the comparison becomes possible.

Averaging prices instead of dividing totals. Cost per share, cost per mile, cost per hire. Add up the money, add up the units, divide once. Averaging the quoted prices only works when you bought the same quantity at each.

Reading a discount as a saving on the thing you wanted. A coupon is only worth what you would have spent anyway. Every offer in this topic is scored against the cheapest way of getting the same goods, which is the only comparison that survives contact with a shop.

Stopping one step early. The catering bill is a third of the wedding. The 16 inch pizza against two 10 inch ones is an area question, and 201 square inches beats 157, because width grows by a factor and area grows by that factor squared. One 16 inch pizza or two 10 inch ones catches almost everyone the first time.

A brochure, a shop owner, and a rule nobody had read

In 2003 a retired shop owner in Michigan picked up a lottery brochure and read the payout rules properly. When a jackpot went unclaimed, the money rolled down into the smaller prize tiers instead of carrying over. On those particular draws, a large enough batch of tickets returned more than it cost.

The odds on any single ticket never moved. The payout side of the arithmetic moved, and only on the handful of draws that rolled down. He bought in bulk on those weeks, kept doing it for years, and the story was later told at length by HuffPost Highline.

The lesson generalizes past lotteries. When an offer looks impossible, the interesting question is usually not the probability. It is which line of the terms nobody bothered to read. A brochure, a retired shop owner, and a roll-down tells it as one card.

Where this shows up

Restaurants and tips, where the tenth-then-double move gets used most. Supermarket shelves, where unit pricing settles arguments that packaging is designed to start. Store finance and buy now pay later, where the cost hides in a discount you declined. Salary negotiations, contractor rates and freelance quotes, where everything has to reach the same unit before it can be compared.

Also the receipts you split with friends, which is where most people find out that they can do this faster than the person reaching for a phone.

Try them one at a time

The feed above holds these questions as cards. One situation, one question, a box for your answer, and a line underneath that names the move which gets there quickly. No timer, no score, no account.

When you want the percent side of the same habit, Percent traps covers discounts, chained cuts and the difference between points and percent. For pure speed on the arithmetic itself, Mental math practice is the shorter, drier set.