Saving and interest
Money in a savings account earns interest from the bank. With compound interest, the interest itself starts earning too, and that makes a big difference over many years.
Why
You put €500 from your summer job into a savings account. How much is in it after ten years if you leave it alone?
Money in a piggy bank at home always stays the same amount. In a savings account, the bank pays you a small fee for being allowed to use your money. That fee is called interest.
The longer you save, the more it matters whether you also get interest on your interest. After a few years you hardly see the difference. After thirty or forty years you see it very clearly.
See it
Choose a starting amount, an example rate per year and a number of years. Compare the straight line of simple interest with the curve of compound interest, which bends upwards.
Simple: €1,600.00 · Compound: €1,806.13
An example rate, not advice. The bank adds the interest every year and rounds to the cent.
Description of the picture
A graph with the years on the horizontal axis and the savings on the vertical axis. Sliders for the starting amount, from €100 to €5,000, the interest rate per year, from 0% to 8%, and the number of years, from 0 to 40. A straight line shows simple interest, a curve that keeps getting steeper shows compound interest. A text gives both final amounts.
Get it
A bank lends the savings of its customers to others, for example to a family buying a house. For that use, it pays you interest. Interest is given as a percentage per year: at 2% you get €2 per year for every €100 in the account.
With simple interest you get interest on your starting amount only, every year. On €1,000 at 3% that is €30 every year. After 5 years you have €1,000+
With compound interest the bank adds the interest to your savings every year. The next year you get interest on the larger amount, so also interest on your interest. After one year you have €1,030, after two years €1,030+
A quick estimate is the rule of 72. Divide 72 by the interest rate in percent, and you know roughly after how many years your money doubles with compound interest. At 3% that is about 72:
The rates in this lesson are examples. Real savings rates change over time and differ from bank to bank. We leave taxes on interest out here. Anyone who promises a much higher return than a savings account is almost always taking a much bigger risk with your money.
Simple: every year interest=
Worked example
Yassin puts €500 into a savings account with an example rate of 2% per year. The bank adds the interest to the amount every year and rounds to the cent. How much is in it after 3 years?
Year 1: 2% of €500 is €10.
€500.00+
€10.00= €510.00 Year 2: now Yassin gets 2% of €510, which is €10.20.
€510.00+
€10.20= €520.20 Year 3: 2% of €520.20 is €10.404, rounded €10.40.
€520.20+
€10.40= €530.60 With simple interest Yassin would have had €530. The interest on the interest brings in 60 cents extra here.
- Answer
After 3 years there is €530.60 in the account.
Do it
Pick a level. You get a new exercise every time, checked straight away. Amounts to the cent.
Pitfalls
Wrong: At 2% interest I get €2 a year.
2% means €2 per €100. On €800 you get €16.
Right: Work out the interest as a percentage of the amount in the account.
Wrong: Compound interest after 10 years is just 10 times the interest of the first year.
That is simple interest. With compound interest the interest grows every year, because the amount grows.
Right: Calculate year by year: add the interest, then the new interest on the new amount.
Wrong: The higher the promised return, the better the place for my savings.
A much higher return almost always comes with a much bigger risk. Crypto, for example, can rise fast but can also fall fast, and it is not a savings account.
Right: Savings belong in a place where they are safe, even if the interest is low.
In real life
- Many parents or grandparents open a savings account for a child. Money put in early has the longest time to grow.
- With the money from a summer job you can set part aside for later, for example for your driving licence or your first student room.
- Savings in a bank are protected up to €100,000 per person per bank. That rule applies across the whole European Union.
- Banks show the yearly interest rate of their savings accounts. Comparing pays off, but read the conditions too.
History
Around 600 BC the first coins were struck in Lydia, a land in what is now Turkey. Before that, people often kept their wealth as grain or cattle, which could rot or die. Coins made it easier to put something aside for later.
At the table
Did you have a savings account or a piggy bank when you were young? What were you saving for, and how long did it take?
A question to talk about together, for parents and young people. There is no wrong answer.