Interest calculation: what it is about
Interest is the price of borrowed money. If you deposit money, the bank pays you interest. If you take out a loan or pay an invoice late, you pay interest. Interest calculation therefore always answers the same question: how much does a certain amount of money cost or earn over a certain period at a certain rate?
This guide explains simple interest as it is used at school, for savings books, overnight deposits, short-term loans and German statutory default interest. Simple means that interest is not reinvested and does not earn interest itself. You can follow every calculation in this article in the interest calculator, which shows the worked solution for each result.
The interest formula
The basic simple interest formula is:
I = P · r · t / 100
The four quantities are:
- I: interest in euros
- P: principal, i.e. the amount deposited or borrowed
- r: interest rate in percent per year (p.a.)
- t: time in years
Dividing by 100 turns the percentage into a decimal: 3% is 0.03. If you prefer decimals, write I = P · i · t with i = r / 100. The result is the same.
A first example: you deposit €2,000 for one year at 2%. Then I = 2,000 · 2 · 1 / 100 = €40. After one year you have €2,040.
Annual, monthly and daily interest
The formula always works in years because rates are almost always quoted per year. If money is invested for more or less than a year, t is adjusted accordingly.
Monthly interest
For months divide by 12: t = months / 12. Example: €5,000 at 2.4% for 7 months gives I = 5,000 · 2.4 · 7 / (100 · 12) = €70.
Daily interest
For days divide by the number of days per year. In Germany, schools and many savings contracts use the German method: the year has 360 days and every month 30 days. This gives the familiar formula for daily interest:
I = P · r · days / (100 · 360)
Example: €10,000 at 3% for 90 days gives I = 10,000 · 3 · 90 / 36,000 = €75. That is exactly a quarter of the annual interest of €300, because 90 days are a quarter of 360.
Depending on the product, banks also count actual calendar days and divide by 360, 365 or 366. Which method applies when, and how big the differences are, is covered in day-count methods compared.
Counting interest days
For a date range, the first day is usually not counted and the last day is. From 1 March to 1 April there are 31 actual days, or 30 interest days under the German method. Under the German method the 31st of a month counts as the 30th, and so does the last day of February. From 15 January to 15 April there are exactly 90 interest days.
Rearranging the formula
In exercises and in real life you often need one of the other quantities rather than the interest. Since the formula only consists of multiplications and one division, it is easy to rearrange.
Solving for principal
P = I · 100 / (r · t)
Question: how much must I invest to earn €120 in half a year at 4%? P = 120 · 100 / (4 · 0.5) = €6,000.
Solving for the rate
r = I · 100 / (P · t)
Question: a €3,000 loan costs €45 interest for six months. What annual rate is that? r = 45 · 100 / (3,000 · 0.5) = 3%.
Solving for time
t = I · 100 / (P · r)
Question: how long must I invest €8,000 at 2.5% to earn €50? t = 50 · 100 / (8,000 · 2.5) = 0.25 years. Times 360 that is 90 interest days, roughly three months.
If you know the rule of three you get the same results: interest is proportional to principal, rate and time. The rule of three calculator helps with such problems, the percentage calculator with plain percentages.
Step by step: solving an interest problem
1. Identify the unknown: interest, principal, rate or time?
2. Convert time into years: days divided by 360 (or 365), months divided by 12.
3. Rearrange the formula for the unknown.
4. Insert the values and calculate.
5. Check plausibility: an annual rate of 300% or a term of 400 years usually means a unit error, typically in t.
The most common mistake is exactly that: days are inserted directly without converting them into years. Using 90 instead of 0.25 gives 360 times the correct result.
Simple versus compound interest
With simple interest the principal stays the same for the whole term. With compound interest, interest is added to the principal at year end and earns interest in the following year. The capital then grows exponentially according to P · (1 + r/100)^n.
Within one year there is no difference. Over long periods it becomes significant: €10,000 at 3% earns €3,000 in ten years with simple interest, and €3,439.16 with annual compounding. The interest calculator shows both curves side by side. For long-term investments, use the compound interest calculator, which also handles monthly savings.
Simple interest is still highly relevant. It applies wherever interest is paid out instead of reinvested, within a year (for example between two interest credits on a savings account) and to German default interest: under § 289 BGB no interest may be charged on default interest itself.
German default interest under § 288 BGB
If an invoice is not paid on time, the debtor is in default. At the latest 30 days after the due date and receipt of the invoice, default occurs even without a reminder; for consumers only if the invoice points this out (§ 286 (3) BGB). From then on the creditor may charge default interest.
§ 288 BGB sets the rate. It is based on the base rate under § 247 BGB, which the Deutsche Bundesbank announces on 1 January and 1 July each year. Since 1 July 2026 it has been 1.52%; in the first half of 2026 it was 1.27%.
- A consumer is involved: base rate + 5 percentage points, currently 6.52% p.a.
- No consumer involved (business to business): base rate + 9 percentage points, currently 10.52% p.a., plus a flat fee of €40 under § 288 (5) BGB.
Example: a €2,500 invoice is paid 60 days late. Against a consumer that is 2,500 · 6.52 · 60 / (100 · 365) = €26.79. Between businesses, at 10.52%, it is €43.23 plus the €40 flat fee. In practice, default interest is usually calculated with actual calendar days and 365 days per year.
If the default period spans 1 January or 1 July, the base rate valid in each section applies. In default-interest mode the calculator splits the period automatically and shows each part separately. The calculation is not legal advice; whether and from when default occurred depends on the individual case.
Common use cases
- Homework and exams: interest problems with 360 days per year, often solving for principal, rate or time.
- Overnight and fixed-term deposits: what does an investment earn over a few weeks or months?
- Private loans and deferrals: what interest is due if an amount is repaid later?
- Unpaid invoices: how much default interest may I charge?
- Comparing offers: what annual rate is hidden in a fee for a certain period?
Conclusion
Simple interest needs just one formula: I = P · r · t / 100. What matters is converting time correctly into years and choosing the right day-count method. For multi-year terms with reinvested interest, compound interest is the right model. The interest calculator solves every variant of the formula with a worked solution, including daily interest and default interest at the current base rate.