Canada has abolished the penny; Sweden is almost entirely cash-free. Are we heading for a future with no notes or coins? And does it matter?

Canada decided to phase out the penny (one cent) coin. Although it will still be legal tender, retailers will have to give any pennies they receive to the Royal Canadian Mint. They will also be encouraged to round to the nearest five cents when giving change. In the longer term, the Mint hopes to replace other coins and notes with a digital currency called MintChip. MintChip will ultimately let people pay each other directly using smartphones, USB sticks, computers, tablets and clouds. The digital currency will be anonymous and good for small transactions — just like cash. Although many dismissed it as a stunt, or even a joke, the competition to write software for MintChip attracted 500 applicants in four days. Meanwhile, Barclays has already developed a system in Britain, called PayTag, which allows users to pay by swiping a sticker on their mobile phone over a reader.

So, why do this? Well, cost is a big part of it. According to the Canadian government, it costs 1.6 cents to produce each one cent new penny. It also notes that inflation has meant that the penny retains only about one-20th of its original purchasing power. Indeed, some Canadians consider the penny more of a nuisance than a useful coin. In 2006, the penny cost Canada's economy about $150m, according to Quebec-based bank Desjardins. Canada's big banks alone handle more than nine billion pennies a year, which costs them $20m annually to process. There is an argument that, by extension, all cash should go. In an era when books, movies and music are transmuting from atoms to bits, those increasingly costly metal rounds are looking more analog by the minute.

America has decided not to follow Canada, instead cutting minting costs by changing the metal content of smaller coins. But many others - including Israel, Brazil, Australia and the Scandinavian nations – already have no penny equivalent. Many governments are also gradually making it harder to pay by cash. France, Greece and Spain have all put limits on the maximum size of cash transactions to try to cut tax evasion. Britain's anti-money-laundering rules  make it difficult to pay more than £10,000 for anything in cash. But no country has gone as far as Sweden in trying to move away from cash.

In Sweden, only around 3% of transactions are now cash-based. In most cities, pubs don't accept cash; tickets are prepaid or purchased with a text message. A small but growing number of businesses only take cards and some bank offices (which make money on electronic transactions) have stopped handling cash altogether. Some even think that coins and notes will cease to exist in Sweden within 20 years. However, not everyone is happy with this trend. Pensioners, who tend to do lots of small transactions, complain that their lives have been made harder. Small businesses are also unhappy about the level of credit-card fees charged by the banks. While the number of bank robberies has dropped, computerised fraud cases, including skimming, surged.

How about the UK? Credit cards and online payment systems, such as PayPal, have failed to kill the global enthusiasm for hard currency. Although cash's role in the total money supply of most developed countries has fallen, it is still important. The Bank of England estimates that £61.8bn of notes and coins are still circulating somewhere in the British economy. Further, if we were to change, between 60% and 93% of transactions would round up, costing consumers nearly $600m a year. Because the poor tend to use cash more often, they would shoulder most of that burden. Therefore, it would be politically unpalatable, so don’t kiss goodbye to your hard copy sterling for a while yet. But it will happen within the next 30 years.