Module 2 · Money maths
Why a euro today beats a euro tomorrow
Present and future value, the cost of the option you give up, real interest rates, and what happened when euro area interest rates went below zero.
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In this lesson
- Explain why money now is worth more than the same amount later
- Calculate future value and present value, and use them to compare money at different dates
- Work out a real interest rate and explain what a negative one means for savers
- Describe why the ECB set negative interest rates from 2014 to 2022
Nika’s grandmother offers her a choice: €1,000 now, or €1,100 in two years. “Take the bigger one,” says her brother. “€100 extra for waiting.” Is he right? The answer depends on something you cannot see in either number: what money can do while you wait.
A euro today is worth more than a euro later
Most people prefer money now to the same money later, and there are good reasons. This idea is called the . It has three parts:
- Interest. Money you have today can be saved and earn interest.
- Inflation. Prices may rise, so the same euros may buy less later.
- Risk. A promise of future money might not be kept.
Every choice also has an : the value of the best option you give up. If Marko keeps €5,000 in a 0% current account instead of a savings account paying 3% a year, he loses no euros. But after 20 years the savings account would hold 5,000 × 1.03²⁰ = €9,031. His opportunity cost is about €4,031.
Future value and present value
The is what money today will grow to. You know this from compound interest:
future value = amount today × (1 + rate)^years
€1,000 at 4% for 5 years: 1,000 × 1.04⁵ = €1,217.
The runs the same calculation backwards. It tells you what a future amount is worth today:
present value = future amount ÷ (1 + rate)^years
Working backwards like this is called . If Nika will receive €10,000 in 5 years and could earn 4% a year, the promise is worth 10,000 ÷ 1.04⁵ = €8,219 today.
Real interest rates
What matters for savers is not the number of euros, but what they can buy. The is the interest rate after inflation:
real rate ≈ interest rate − inflation
A deposit pays 2.5% while prices rise 3.8%. The real rate is about 2.5 − 3.8 = −1.3%. Your balance grows, but its purchasing power shrinks.
The exact formula is (1 + interest rate) ÷ (1 + inflation) − 1. Here: 1.025 ÷ 1.038 − 1 = −1.25%. The quick rule is fine when rates are low. When they are high it goes wrong. At 50% interest and 40% inflation, the quick rule says 10%, but the exact answer is 1.50 ÷ 1.40 − 1 = about 7%.
When interest rates went below zero
From June 2014 the ECB did something unusual: it set its deposit rate below zero. Banks had to pay to keep extra money at the central bank. Inflation was very low and the economy was weak. The ECB wanted to push banks to lend money to households and firms instead of keeping it parked.
The deposit rate fell step by step from −0.10% in 2014 to −0.50% in September 2019. It returned to 0% in July 2022, when inflation was rising fast, and reached 4.00% in September 2023. After cuts that began in 2024, it rose again in 2026 to 2.50% from 16 September.
Most ordinary savers were never charged negative interest. They mostly earned close to 0%, and some banks charged fees on very large balances. But with prices still rising, their real interest rate was negative for years.
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