The rate you get and the rate you keep
- Start£100After a year£104
Pounds in the account. Put £100 in a savings account. The bank pays 4% a year for keeping it there. That payment is called interest. After a year the account shows £104. The bank kept its promise: four more pounds.
- £104Pounds in the account£106Last year's £100 of shopping now costs
In that same year prices rose 6%. The shopping that cost £100 last year now costs £106. The account holds £104. So the savings buy a little less than they did a year ago, even though the number went up.
- Your savings grew4%Prices rose6%
Your savings pay 4% a year. Prices rise 6% a year. After a year, what can your savings buy?
4% more. The account paid 4%.
Not yet. It paid 4% more pounds. The shop now wants 6% more pounds for the same shopping. Interest is counted in pounds, and pounds are what got weaker.About 2% less than before.
Right. You have 4% more pounds and every pound buys 6% less. The gap is what you actually kept, and this year it is negative.The same. The money is safe in the bank.
Not yet. Safe in pounds, yes: the bank will not lose one. But what those pounds buy is not stored anywhere, and it fell about 2%. - Interest the bank paid4%Prices rose6%The real rate−2%
Take the price rise off the interest rate. What is left is called the real rate. Real just means measured in shopping, not in pounds. Four minus six is minus two. The bank says 4%. The saver keeps −2%.
- Interest earned2%Prices rose5%
Savings earn 2%. Prices rise 5%. Roughly what is the real rate?
% a yearInterest minus inflation. It can be negative.
Right. Minus three. The exact figure is 1.02 divided by 1.05, about −2.9%, and the simple subtraction is close enough for any rate under ten. The 2% is what the bank says. The −3% is what the saver keeps. Four accounts, four different years. Tap the one whose money bought MORE at the end of the year.
Tap the part of the picture that answers it.
Take the price rise off each interest rate.
Paid 1% in a year prices rose 2%1%Paid 5% in a year prices rose 9%5%Paid 3% in a year prices rose 2%3%Paid 0% in a year prices rose 1%0%The interest each account paid. Paid 3% in a year prices rose 2%
Right. The only one ahead of prices: a real rate of about +1%. Smaller than the 5% the second account paid, and the only account that ended the year able to buy more.Paid 1% in a year prices rose 2%
Not yet. One point behind prices. The money bought about 1% less at the end of the year than at the start.Paid 5% in a year prices rose 9%
Not yet. The biggest interest rate and the biggest loss: four points behind prices. A high rate in a high-inflation year is a bigger number that buys less.Paid 0% in a year prices rose 1%
Not yet. Cash in a drawer. One point behind, quietly. It never looks like a loss because the number never moves.- Pounds in the account after ten years£148What they buy, in today's shopping£83
A gap of two points sounds small. But it stacks every year, the same way prices did in the last lesson. Ten years at 4% while prices rise 6%: the account grows to £148. That £148 buys what £83 bought at the start. The number went up the whole time.
£100 in a savings account for ten years. Set what the account pays, and how fast prices rise.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 0% · Prices rise by: 0%
£100 saved at 0% while prices rise 0%. After ten years: It holds its value exactly.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 0% · Prices rise by: 2%
£100 saved at 0% while prices rise 2%. After ten years: It shrinks: worth £82.0 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 0% · Prices rise by: 4%
£100 saved at 0% while prices rise 4%. After ten years: It shrinks: worth £67.6 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 0% · Prices rise by: 6%
£100 saved at 0% while prices rise 6%. After ten years: It shrinks: worth £55.8 of today's shopping.
£0£68£137Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 2% · Prices rise by: 0%
£100 saved at 2% while prices rise 0%. After ten years: It grows: worth £121.9 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 2% · Prices rise by: 2%
£100 saved at 2% while prices rise 2%. After ten years: It holds its value exactly.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 2% · Prices rise by: 4%
£100 saved at 2% while prices rise 4%. After ten years: It shrinks: worth £82.4 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 2% · Prices rise by: 6%
£100 saved at 2% while prices rise 6%. After ten years: It shrinks: worth £68.1 of today's shopping.
£0£83£166Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 4% · Prices rise by: 0%
£100 saved at 4% while prices rise 0%. After ten years: It grows: worth £148.0 of today's shopping.
£0£68£136Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 4% · Prices rise by: 2%
£100 saved at 4% while prices rise 2%. After ten years: It grows: worth £121.4 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 4% · Prices rise by: 4%
£100 saved at 4% while prices rise 4%. After ten years: It holds its value exactly.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 4% · Prices rise by: 6%
£100 saved at 4% while prices rise 6%. After ten years: It shrinks: worth £82.7 of today's shopping.
£0£100£201Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 6% · Prices rise by: 0%
£100 saved at 6% while prices rise 0%. After ten years: It grows: worth £179.1 of today's shopping.
£0£82£165Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 6% · Prices rise by: 2%
£100 saved at 6% while prices rise 2%. After ten years: It grows: worth £146.9 of today's shopping.
£0£68£136Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 6% · Prices rise by: 4%
£100 saved at 6% while prices rise 4%. After ten years: It grows: worth £121.0 of today's shopping.
£0£56£112Year 0Year 10What the savings buy, measured in today's shopping. Your savings earn: 6% · Prices rise by: 6%
£100 saved at 6% while prices rise 6%. After ten years: It holds its value exactly.
When does saving make you better off in what you can BUY?
Whenever the account pays interest.
Not yet. At 4% interest and 6% prices the account paid every year and the line still fell. Interest below the price rise still loses, only more slowly.Whenever prices rise slowly.
Not yet. At 0% interest and 2% prices the line falls. Prices rising slowly is not enough. They have to rise more slowly than the interest.Only when the rate you earn is above the rate prices rise.
Right. The line climbs above £100 only when the interest number is bigger than the prices number. When the two match it is flat. When interest is smaller, the savings shrink a little every year.Move both controls.
£100 saved at 4% while prices rise 6%. Move through the years.
Pounds in the account£104What they buy, in today's shopping£98.10Years saved: 1 year
The account shows £104. It buys what £98.1 buys today.
Pounds in the account£121.70What they buy, in today's shopping£90.90Years saved: 5 years
The account shows £121.7. It buys what £90.9 buys today.
Pounds in the account£148What they buy, in today's shopping£82.70Years saved: 10 years
The account shows £148. It buys what £82.7 buys today.
Pounds in the account£219.10What they buy, in today's shopping£68.30Years saved: 20 years
The account shows £219.1. It buys what £68.3 buys today.
Pounds in the account£324.30What they buy, in today's shopping£56.50Years saved: 30 years
The account shows £324.3. It buys what £56.5 buys today.
The pounds in the account tripled over thirty years. Why is the second bar going down?
The bank took fees.
Not yet. No fees in this example. The account paid its full 4% every year, and the shopping still shrank.Prices grew faster than the pounds did, so each pound lost more than the new pounds added.
Right. Prices and the savings both stack up every year. Prices stack faster, at 6% against 4%. After thirty years the account holds three times the pounds, and they buy a bit more than half the shopping.The interest was not compounded.
Not yet. It was. That is why the pounds tripled. Prices compounded too, and at 6% they compound faster than 4% does.Move the control.
- Interest paid5%Prices rose7%
In 2023 many UK savings accounts paid around 5%, the best in fifteen years. Prices rose about 7% over that year. Was a saver better off in what they could buy?
Only if they saved for the whole year.
Not yet. Timing changes how much of the gap they felt, not which way it ran. A rate behind prices loses over any stretch it is held.Yes. Five per cent is a lot of interest.
Not yet. Five is a lot compared with the 1% of the years before. It is not a lot compared with the 7% the shops wanted, and that comparison is the one that decides what the savings buy.No. The best rate in fifteen years still trailed prices by about two points.
Right. The account paid the best interest in fifteen years. The shops wanted 7% more. The saver ended the year able to buy about 2% less.
Lesson complete
Savings grow only by the gap between interest and inflation, and that gap can be below zero.