Inflation calculator

[MDW1954]

I occasionally need to work out the impact of a given rate of inflation on purchasing power at a point in the future.

Most times I just do it manually "long-hand" with a calculator, or -- if I'm feeling clever and can remember to enter the formula correctly in my calculator -- by raising to the power. (eg, 1 x 0.95 raised to the 25th for 5% inflation over 25 years).

The other day I sat down to tweak a bit of old BASIC code that calculates compound growth rates. Inflation, after all, is just negative growth.

What I've noticed is that having checked the result against pencil and paper/ calculator AND a few online calculators, I get results that differ from the online sites, but not my long-hand calculations.

Somewhere, years ago, I saw a figure from Hargreaves Lansdown which said that with 4.5% inflation, your purchasing power would halve after 16 years. I used this as the test. I get £1 reducing to £0.479 after 16 years (0.478689), while the online sites seem to prefer 0.49447 -- not a huge difference, but probably not one that can be explained by double precision variables etc.

Here's an example:

https://www.rl360.com/row/tools/inflation-calculator.htm?Currency=0&AmtSaved=1000&YrsToKeep=16&InflRate=4.5&Calculate=Calculate

Now, I'm quite happy to accept that I'm doing something wrong, although for the life of me I can't think what.

Any thoughts, anyone?

MDW1954

[scrumpyjack]

Not quite sure what you are doing but it is very simple

100 and 4.5% inflation is 104.5 at the end of year 1
at the end of year 2 it is 109.2025
at the end of year 16 it is 202.2370153

100 is then 49.45% of 202.2370153

[mc2fool]

Any thoughts, anyone?

(Do I have a sense of deja vu here...? )

You are looking at it upside down. Inflation is about the increase of the cost of goods, rather than the decrease in money. That may sound like two sides of the same coin but it's not in doing the maths.

Try this: if you can currently get 1000 gobstoppers for £100, and gobstopper inflation is 4.5% over the next year, how many gobstoppers will you then get for £100? Hint: it's not 955.

Your math for 16 years @ 4.5% is 1 - 4.5%, i.e. 0.955 raised to the power of 16, which = 0.47868954844692669363421067800579

What you should be doing is 1 / (1.045 ^ 16) = 0.4944693227902078137066298992675

This all becomes rather obvious if you plug in large numbers -- by your method if you had inflation of 100%pa you'd be raising zero to the nth power.

[MDW1954]

Any thoughts, anyone?

(Do I have a sense of deja vu here...? )

Nope. Not from me, anyway. I've posted other questions here, but not that one.

Thank you! Two glasses of wine to the good, I'll figure out the maths in the morning. But I did want to express my thanks, and say "mission accomplished".

MDW1954

[MDW1954]

Not quite sure what you are doing but it is very simple

100 and 4.5% inflation is 104.5 at the end of year 1
at the end of year 2 it is 109.2025
at the end of year 16 it is 202.2370153

100 is then 49.45% of 202.2370153

Scrumpyjack,

Yes, it had occurred to me that the "right" answer was the reciprocal of the compound growth equivalent, ie 2.022370153 -- yet somehow, that didn't prompt what is in retrospect a fairly obvious realisation.

So many thanks to you, too.

MDW1954