Welcome to your study space
Understand economics at your own pace: step-by-step guided courses, and exercises to practice.
What is a central bank?
The keeper of prices, who makes credit dearer or cheaper.
annual interest = amount borrowed × rateProblem / motivation
You often hear that “the European Central Bank has raised its rates”. But what is a central bank actually for — and first of all, what is a “rate”?
Two words before anything else. When you borrow, you pay back the sum PLUS something extra: INTEREST — the rent on money. The INTEREST RATE is that extra expressed as a % per year: borrowing €100 at 3% means handing back €103 in a year. A rate, then, is the PRICE of money. A CENTRAL BANK, for its part, is not a bank where you open an account: it is the public institution that watches over the currency of a whole area — the ECB for the euro (decisions taken by the Governing Council, in Frankfurt), the Fed for the dollar.
Its mission number one: keeping prices STABLE. Mind the word: “stable” does not mean zero — the target is a rise of about 2% A YEAR, low enough for the currency to keep its value, but not nil, so as to drive well clear of the ditch of deflation (the course “What is deflation?” explains that danger). To hold that target, it has a lever of disarming simplicity: making credit dearer or cheaper. This course builds that lever; the next one (“The policy rate and transmission”) follows its spread all the way to prices.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Take the opening example again: €100 borrowed at 3% is €3 of interest over the year. Generalise: the interest paid over a year is the amount multiplied by the rate — interest = amount × rate. That is the whole formula of this course, and it is enough: the rate turns a borrowed sum into a concrete cost.
Where does YOUR rate come from? Your bank starts by funding itself — notably from the central bank, at the POLICY rate (assumption 2) — then lends to you at a higher price: its margin. When the policy rate goes up, your rate follows; when it comes down, so does yours (for NEW loans). There is the bridge between its rate and yours — the next course details it link by link.
All the central bank's power sits there: by moving ONE rate, it moves the cost of ALL new credit in the area — hence spending, hence, with a one- to two-year lag, the rise in prices (assumption 4). One dial in Frankfurt, millions of buying decisions shifted. Click each term:
Solving / calculation
You borrow €10,000 for one year (a toy: repaid in one go at the end of the year — a real loan is spread out, the idea holds). Look at what the central bank's decision changes, then work the two scenarios in the simulator.
- Low rate (the central bank has cut its policy rate)
interest = 10,000 × 1%= €100 - High rate (it has raised it, and your bank has followed)
interest = 10,000 × 4%= €400 - Extra cost of the loan caused by the rise
400 − 100= €300 more a year - And the total repaid?
10,100 → €10,400+€300, that is 3% of the capital borrowed — the CREDIT itself costs 4 times more
The INTEREST quadruples (100 → €400); the total repaid, though, rises by only €300 — 3% of the capital borrowed. That is precisely the lever: the central bank does not make money unaffordable — it makes credit dear enough to give pause. Multiply those second thoughts by millions of borrowers: spending slows, and the rise in prices with it.
annual interest = amount × rateTwo scenarios side by side: the rate BEFORE and AFTER the decision (your bank follows, margin included — next course). Then run the experiment that teaches something: move the AMOUNT borrowed. The euros change completely, but the “interest multiplied by” line and the “as a % of capital” line do not budge by one hundredth — because the multiplier depends only on the two rates, and the weight on the capital only on the GAP between them. From 1% to 4%, that is ×4 on the interest and 3% more of the capital: two ways of describing the SAME movement, and they do not have at all the same effect — that is where persuasion is decided, in a newspaper as in a loan negotiation.
Economic interpretation
One dial, three readings: which way the lever works, how slow it is, and everything else the central bank does.
When prices run away, the central bank raises its rate: loans become dearer, households and firms put off their credit-financed purchases (housing, cars, machines) — spending slows, and sellers facing fewer buyers stop raising their prices. That is WHY spending less calms inflation: prices rise when demand pushes, and settle when it eases off.
When activity stalls, it cuts its rate: credit becomes cheap again, people dare to borrow, activity picks up. In both directions, the effect takes ONE TO TWO YEARS to work through (assumption 4): the central bank drives looking far ahead, on forecasts — the course “The policy rate and transmission” puts a figure on each stage of the journey.
“Central bank” does not boil down to the rate. It is the bank that ISSUES the notes (a monopoly on issue — nobody else prints the euro); it is the FIRE BRIGADE for banks (lender of last resort: in a panic, it lends massively to put the fire out); and it SUPERVISES the soundness of the large banks. This course has followed mission number one — prices — but the institution wears all three hats permanently.
Limits / critiques
Exercises
You borrow €12,000 for one year at 2.5%. How much interest do you pay (in €)?
Inflation climbs clearly above the 2% target. To calm it, the central bank will rather…
Why is the target ~2% a year, and not 0%?
You borrow €20,000 for one year at 3% (a toy: repaid in one go). What TOTAL do you repay (in €)?
Same loan (€12,000), but the central bank has raised its rate and yours goes to 4%. What ANNUAL extra cost (in €)?
True or false: a cut in the policy rate makes NEW loans cheaper.
Why is the central bank INDEPENDENT of the government?
True or false: a rise in the policy rate slows the rise in prices from the following month.