How do i calculate annualised inflation rates?

Question

Ok, so if inflation is 3% year on year for 5 years, and a bar of chocolate is £1 at the start of year 1, it will be £1.03 at the start of year 2 - that's straightforward enough.

Then for year 3 that same bar will be 3% of £1.03 which is £0.0309, so that it now costs £1.0609.

However, what is the forumla used so that, if we have the rate of inflation year on year, for each year in a sequence, we can look at what a good cost in year 1, and work out what it would cost to buy that same good in real prices further down the line (or vice versa, work out how inflation has increased prices and work out what they would have cost some time in the past if we have the necessary inflation data).

WHat i want to know is, is there an accurate way to have an annualised inflation rate worked out for a set of years where we have the year on year inflation that will allow us to work out the compounded affect of inflation, either up or down the scale?

Cheers!

Thanks.

Answer 1

Projecting ahead from a value of (say) 100 the first year:
- You're just about there. Keep in mind that 100% of 100 equals 100 (note that's not 100% MORE than 100, it's 100% OF 100, a zero percent increase.)
- In math notation that is 100 X 100% = 100.
- If you convert 100% to a decimal number, that is 1.00
- So, 100 X 1.00 = 100, which equals 100% of 100.

- I lay this out to make clear that if we talk about a 3% INCREASE, we mean 100 X 103% .... or 100 X 1.03 = 103.
This makes it easy to deal with growth or inflation rates.

- So let's say inflation (or expected growth etc) varies over several consecutive years to equal 3%, 4%, 3.5%, 4%, 2% ...

- Then the math is easy, just think of your original number progressively getting larger year to year:
100 X 1.03 X 1.04 X 1.035 X 1.04 X 1.02 = 117.61

- But if instead you have a constant growth rate each year of 3%, then there is a quicker way to calculate it:
100 X 1.03 X 1.03 X 1.03 X 1.03 X 1.03 can be reduced to:
100 X (1.03)^5 = 115.9.

So if i say you'll have 3% inflation for five years, just think of that.

- Going backwards is trickier, but doable. Say you know you started at 100, & five years later you end up at 115.9, but don't know the growth rate.

- Looking back to the previous equation, you have 100 x (Y)^5 = 115.9. You want to solve for Y.

- rearrange the equality and you have Y^5 = 115.9/100 = 1.159. That makes sense, obviously you are multiplying 100 by 1.159 to end up with 115.9.

- So to get Y, you need to find the 5th root of Y^5, which means you need to calculate the 5th root of 115.9:
Y = (Y^5)^(1/5) = 1.159^(1/5)

- That's what your calculator is for: 1.159^(1/5) = 1.03.
(I've been rounding a bit in case you get 1.0299...)

- recall that that factor 1.03 means a growth RATE of 3%. At the end of the above process you subtract 1, to be left with the growth rate in decimal form. .03 = 3%

The growth rate then is Y-1, and you take the supplied information to solve for Y, then subtract your 1.

Answer 2

Yes, what you seem to be looking for is a variation on the compound interest formula. It would be principal x (1+rate of inflation)^n. Principal in this case would be the 1 pound. Rate of inflation is 3%, or .03. and n is the number of years, or 5.

Hope this helps.