# How to calculate cash loss over time?

For example, I got £100 few months ago and I didn't spend them - just kept them in my drawer at home. I understand that those £100 from few months ago is not worth same £100 but it is less today. How exactly I can calculate current money value which I kept from the past?

If inflation is at 2% per annum, in a year you would need £102 to buy equivalent goods to what you could buy today. So if you keep your money in a drawer the buying power of your £100 in a year will be only 100/102 = 98.039% of what it is currently.

• And what if I want to calculate value for few months and not for a year? Also could you help me to find United Kingdom's inflation rates? Jun 29, 2014 at 0:20
• @LukasGreblikas inflation rates are statistical numbers, but what you really lost is the difference between the price of what you bought with the £100 when you did, and the price of that same thing when you put the £100 in the drawer. On average for the whole population this difference is the inflation rate. But for you personally it is an exact and quantifiable number, which may differ significantly from the "general" inflation statistics. Jun 29, 2014 at 0:48
• For the 2% example, the inflation for `n` months is `(1 + 0.02)^(n/12) -1`. You can find inflation figures here: Retail Prices Index and Consumer Price Index Jun 29, 2014 at 9:28

While it is a true loss, as you've determined, is not a cash cost, per se.

A cash cost would be a decrease in cash holdings. Inflation does not take your cash balance; it devalues it, so it is an accrued loss.

Central banks are extremely lazy in determining inflation, so the highest resolution available at a public level is monthly. In the United States, there is a small project that tries to calculate daily inflation rates and seems to do a decent job, but unless if you are a customer of a particular financial institution, you will suffer a lag. The small project refuses to make the data public in real time or even allow outside analysis.

In the UK, the Office for National Statistics is responsible for consumer inflation statistics. The methodology is not readily available, but considering the name, it is most likely an inferior Laspeyres index instead of the optimal Fisher index as it is in the US.

To calculate the accrued cost due to inflation, simply multiply the amount of money held by the price index value at the beginning of the time held and divide by the price index value at the end of the time held.

For example, to determine the amount of value lost since March 2014, multiply the money held by the price index value for March 2014 and divide by June 2014.

• Inflation in too small time periods is not an economic measure. It is affected by weather, various localized effects, seasonal changes, etc. You may see a spike in milk prices because some batch of milk was defective and there was shortage for a week, but then it goes down. That's not "inflation". If it has been a spike long enough to be noticeable for a whole month or, even more accurately, a year - then you can probably say that the prices have risen due to inflation and it is no longer a "spike" but a "climb". Jun 29, 2014 at 6:33
• @littleadv Inflation is always an economic measure regardless of time between samples. It is only affected by changes in the quantity of money, production, and the velocity of money. Inflation of a single product is not inflation. Inflation is not imaginary or unnoticed until a year has passed; it always exists so long as the `|change in prices| > 0` across the time sampled.
– user11865
Jun 29, 2014 at 19:17
• Your statement is wrong. Mods asked me not to engage you, so I won't. -1 for a wrong answer. Jun 29, 2014 at 22:47
• @littleadv Your statements are not backed by any credible economic analysis. All legitimate economists agree that the quantity theory of money is correct; the only disagreement is the ideal rate of inflation.
– user11865
Jun 29, 2014 at 23:14
• Again - you're wrong. Measuring price changes day after day is not a measure of inflation. You must make a measurement so that it will filter out the unrelated interference, and only sustainable price changes can be attributed to inflation. Since in your answer you were talking about price changes as a measure for inflation - claiming that daily changes are meaningful is plain wrong. You're more than welcome to continue this discussion with yourself. -1 stays. Jun 29, 2014 at 23:16

It helps to put the numbers in terms of an asset. Say a bottle of wine costs 10 dollars, but the price rises to 20 dollars a year later. The price has risen 100%, and your dollars have lost value. Whereas your ten used to be worth 100% of the price of bottle of wine, they now are worth 50% of the risen price of a bottle of wine so they've lost around 50% of their value.

Divide the old price by the new inflated price to measure proportionally how much the old price is of the new price. 10 divided by 20 is 1/2 or .50 or 50%. You can then subtract the old price from the new in proportional terms to find how much value you've lost. 1 minus 1/2 or 1.00 minus .50 or 100% minus 50%.

• The inflation rate that governments use is really just the change in price of a basket of physical goods, so it's confusing to say that my dollars went from 100 to 102 from inflation because it's really the price of physical goods in terms of dollars that's rising Feb 24, 2015 at 3:44

There are two things you need to keep in mind when you look at Inflation as an entity.

1. Inflation is necessary to keep in check the value of goods. As per Moore's Law for example, a mobile phone that you buy for £100 today will be available for £50 in two years. With increased purchasing power, one needs to maintain balance between the purchasing power and its value. If you think about the 'loss' at a rate of 2% you would have £96.04 (in terms of today's value) in two years. But if you looked at the same cell phone as leverage for your business where it allowed you to do work and earn £1000 in two years - the investment would clearly offset the cost of inflation.

2. Inflation is incentive for people to spend their money. If you for example spent all of your £100 today, it is £100 income for someone else. He has further incentive to spend it creating a chain of transactions.

In theory while this is a true mathematical loss, the increasing purchasing power helps you leverage your financial asset to get a return on your investment.

• Inflation does not "keep in check the value of goods" and has no necessity. Technological deflation is a tiny fraction of general inflation. Inflation erodes the rate of return on investment and depresses the valuations of investment assets. You are correct however that inflation encourages spending in favor of investment since investment provides less marginal value. Further, inflation decreases purchasing power. Deflation increases it, but that doesn't matter because loans become more onerous, making depressions worse.
– user11865
Jun 29, 2014 at 7:16
• I admit that there must be multiple views on this. My view and opinion was based on this TedEd video Jun 29, 2014 at 7:18
• Yes, there are, just like with global warming, but the science only has one conclusion: inflation is caused by changes in the supply of money, production, and the velocity of money. That video until about 3:00 substantiates my comment. It goes off the rails from there. youtube.com/watch?v=GJ4TTNeSUdQ
– user11865
Jun 29, 2014 at 7:27
• This really doesn't answer the question at all. Feb 24, 2015 at 16:35