Lesson 05 · 4 min · 6 things to do
The rate you get and the rate you keep
Work out a real return from a stated one.
- Interest paid on savings4%Rise in prices6%What the saver actually gained−2%
The third bar is the only one that buys anything. A savings account pays 4% a year. Prices rise 6% that year. What happened to the saver?
- Yes.Both things are true at once, which is why the loss is so easy to miss: the statement shows a gain and the trolley shows a cut.
- Not quite.Breaking even would need the interest to match the price rise. Here it falls two points short, every year, quietly.
- Not quite.They lost the GAP, not the whole rate. Losing 2% of your buying power is bad; losing 6% would be worse.
The number on the account is the NOMINAL rate. Take the price rise off it and you get the REAL rate — the only one that buys anything.
An account pays 5% a year. Prices rise 3%. What is the real rate, in percent?
%Yes.Subtract one from the other. It is an approximation — the exact answer is 1.94% — and it is close enough for any decision until rates get very high.Which of these savers gained ground, and which lost it?
Earns 1% interest. Prices rise 0.5%.
Earns 9% interest. Prices rise 11%.
Earns 0% interest. Prices fall 2%.
Earns 5% interest. Prices rise 5%.
Earns 12% interest. Prices rise 4%.
Yes.The size of the interest tells you nothing on its own. 9% can be a loss and 1% can be a gain — only the gap decides. The 5%-against-5% case is a real loss once tax takes a slice of the interest.The account pays a fixed 4%. Slide the price rise and watch what the saver actually keeps.
0%2%4%9%Interest4%Prices0%Kept4%0%The whole 4% is real. £1,000 buys £1,040 of the same goods next year.
Interest4%Prices2%Kept2%2%Half of it survives. This is roughly what a calm decade looks like.
Interest4%Prices4%Kept0%4%Nothing is kept. The balance grows and buys exactly what it did.
Interest4%Prices9%Kept−5%9%The saver is 5% poorer while the statement shows a gain every month.
The interest never changed across those frames. Why did what the saver keeps change so much?
- Yes.A fixed rate is a fixed number of pounds, not a fixed amount of buying power. The other side of the swap moves whether the account does or not.
- Not quite.It is 4% in every frame. Nothing on the account side moved at all.
- Not quite.Saving is delayed spending. Whatever happens to prices in the meantime happens to the saving.
Move the control to see what changes.
A bond promises to pay back exactly £10,000 in ten years. What is guaranteed?
- Yes.Every fixed promise in money is a promise about the numeral. The buying power that arrives with it is settled by ten years of prices nobody has seen yet.
- Not quite.£10,000 is a name for a quantity of pounds. Its value is whatever it can be swapped for on the day it arrives.
- Not quite.Not defaulting guarantees the numeral. Inflation is the risk that survives even when everybody keeps their promise.
In a year when prices rise 5%, a union settles at 3%. What has been agreed?
- Yes.Both sides can announce it honestly — the employer as a rise, the members as a loss — because the words describe the nominal number and the feeling describes the real one.
- Not quite.That would need prices to stand still. Against a 5% year, 3% loses ground.
- Not quite.A rise smaller than the price rise buys less than last year's pay did. The direction of the number is not the direction of the outcome.
Lesson complete
Only the gap between interest and inflation buys anything.
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