Calculating salary loss from inflation

Question

When it comes to inflation, I simply know that it is an increase in prices that results in a fall of the currency's value. I'd like to apply this to wages in a workplace that has not provided a pay rise for a few years, and to understand any associated formulas.

For example, assume a monthly salary of 10 000 in some currency, with an annual inflation rate of 5%. Now if the pay rise is nil, that would effectively be considered a pay cut, as far as currency value is concerned, correct? Would it also be a correct assumption that any raise between 0% to 5% in this case would still be considered a pay cut, as the pay rise would need to be greater than the inflation rate to have any real value?

How would one calculate the loss in value over multiple years?

Answer 1

Now if the pay rise is nil, that would effectively be considered a pay cut, as far as currency value is concerned, correct?

Correct. Expenses go up at an exponential rate, but your salary stays the same.

Would it also be a correct assumption that any raise between 0% to 5% in this case would still be considered a pay cut, as the pay rise would need to be greater than the inflation rate to have any real value?

Also correct, since your salary would not keep up with the increase in prices.

How would one calculate the loss in value over multiple years?

https://money.stackexchange.com/a/33763/22266

"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."

Do that every year:

Year   Formula            Value
0                         $10,000
1      $10,000*(1/1.05)    $9,524
2      $10,000*(1/1.05^2)  $9,070
3      $10,000*(1/1.05^3)  $8,638
4      $10,000*(1/1.05^4)  $8,227

Answer 2

Yes, your statements are correct.

To see what your effective rate of pay is given inflation, DIVIDE by 100% plus the inflation rate. Many people mistakenly subtract.

That is, say that inflation is 5%. You are presently making 100 foobars a month. Many people think this is the equivalent of now making 100 - 5 = 95 foobars. That's incorrect. It's the equivalent of 100 / 1.05 = 95.2 foobars.

Okay, with relatively small numbers, tiny difference. But suppose the inflation rate is 100%. That is, prices double. That is definitely NOT the equivalent of you now making 100 - 100 = 0! You're still making something. Rather, it's 100 / 2.00 = 50. You're money is worth half as much.

For multiple years, you have to multiply the inflation rates for each year together. For example, 10% each year for 5 years is not 10 + 10 + 10 + 10 + 10 = 50. It's worse than that. Its 1.10 x 1.10 x 1.10 x 1.10 x 1.10 = 1.61, that is, 61%. Each year builds on the previous year.

It's easier to do multi-year calculations if you have statistics keyed to some base year. Like if they say, 1990 is 100%, and then give all other years as some percentage of that.