What is the interest formula?

The basic simple interest formula is I = P · r · t / 100, where I is the interest, P the principal, r the annual rate in percent and t the time in years. For daily interest use t = days / 360 (German method) or days / 365; for months, t = months / 12. Example: €10,000 at 3% for 90 days gives 10,000 · 3 · 90 / (100 · 360) = €75.

How do I calculate daily interest?

Daily interest is I = P · r · days / (100 · 360) under the German method, or with 365 in the denominator under act/365. First count the interest days: under 30/360 every month has 30 days, act methods use actual calendar days. The deposit day usually does not count, the final day does. The calculator above counts the days for you from two dates.

How do I rearrange the formula for principal, rate or time?

From I = P · r · t / 100 there are three rearrangements: principal P = I · 100 / (r · t), rate r = I · 100 / (P · t) and time t = I · 100 / (P · r). Time t comes out in years; multiply by 360 for interest days under the German method or by 12 for months. Just pick the unknown in the calculator — the worked solution shows each step.

What is the difference between simple and compound interest?

With simple interest, interest is calculated only on the original principal and not reinvested. With compound interest, interest is added to the principal and earns interest the following year. Within one year the result is the same; over many years compound interest grows much faster. For multi-year investments with reinvestment, use our compound interest calculator.

What is the German day-count method (30/360)?

Under the German method, also called commercial interest calculation, every month has 30 days and the year 360 days. The 31st of a month counts as the 30th, as does the last day of February. From 15 January to 15 April there are exactly 90 interest days. It is common at school and for savings books; banks often use act/360 or act/365 for overnight savings and loans.

How high is German default interest in 2026?

German default interest follows § 288 BGB: base rate plus 5 percentage points if a consumer is involved, plus 9 points for transactions without a consumer. According to the Bundesbank the base rate has been 1.52% since 1 July 2026, giving 6.52% p.a. for consumers and 10.52% p.a. for businesses. In the first half of 2026 the base rate was 1.27%, i.e. 6.27% and 10.27%.

When does the base rate change?

The base rate under § 247 BGB changes on 1 January and 1 July each year, by as many percentage points as the ECB main refinancing rate has moved since the last adjustment. The Bundesbank publishes the new value in the Federal Gazette. If a default period spans a change date, our calculator applies the rate valid for each section.

Can I use the interest calculator for homework?

Yes. For every problem the calculator shows the basic formula, the rearrangement for the unknown, the inserted values and the result — just like in maths class. Set the method to 30/360 if your exercise uses 360 days a year, which is standard in German textbooks. Use it to check your own answer.

Simple Interest: 6 Exercises with Solutions | Interest Calculator

Practising simple interest

Simple interest is part of the lower secondary curriculum and appears in tests, final exams and commercial training. The six exercises in this article cover all typical questions: interest, daily interest, principal, rate, time and starting capital. All exercises use the German method with 360 days per year and 30 days per month, as in most German textbooks.

Try to solve each exercise yourself first. You can then check your answer against the solution or in the interest calculator, which shows the worked solution step by step.

The formulas at a glance

Interest: I = P · r · t / 100
Principal: P = I · 100 / (r · t)
Rate: r = I · 100 / (P · t)
Time: t = I · 100 / (P · r)

Time t is always in years. Divide months by 12 and days by 360.

Exercise 1: interest for months

Ms Kaya invests €4,500 for 8 months at 3.5%. How much interest does she receive?

Solution: t = 8 / 12. I = 4,500 · 3.5 · 8 / (100 · 12) = €105.

Exercise 2: daily interest with dates

A balance of €7,200 earns 2.5% from 10 March to 25 June. Calculate the interest.

Solution: Interest days under the German method: March to June are 3 full months (90 days), plus 15 days from the 10th to the 25th, 105 days in total. I = 7,200 · 2.5 · 105 / (100 · 360) = €52.50.

Exercise 3: find the principal

What principal earns exactly €84 interest in 150 days at 2.8%?

Solution: P = I · 100 · 360 / (r · days) = 84 · 100 · 360 / (2.8 · 150) = 3,024,000 / 420 = €7,200.

Exercise 4: find the rate

Mr Braun pays €270 interest over 9 months on a €12,000 loan. What is the rate?

Solution: t = 9 / 12 = 0.75. r = 270 · 100 / (12,000 · 0.75) = 27,000 / 9,000 = 3%.

Exercise 5: find the time

For how many days must €6,400 be invested at 3.75% to earn €60 interest?

Solution: t = 60 · 100 / (6,400 · 3.75) = 6,000 / 24,000 = 0.25 years. Times 360 that is 90 days.

Exercise 6: starting capital from the final amount

Including interest, a principal has grown to €5,125 in 200 days at 4.5%. What was the starting principal?

Solution: The final amount is P · (1 + r · t / 100). With t = 200 / 360: 1 + 4.5 · 200 / 36,000 = 1.025. P = 5,125 / 1.025 = €5,000. The interest is therefore €125.

This one is tricky: simply deducting 4.5% from €5,125 is wrong, because the rate refers to the starting principal, not the final amount.

Typical mistakes in tests

Time not converted: 105 days are used directly as t instead of 105 / 360.
Interest days miscounted: under the German method every month has 30 days, February included.
Percent divided twice: if you use r = 0.035, do not divide by 100 again.
Final amount confused with interest: often only I is asked for, not P + I.

A good test is a plausibility check: if the rate comes out above 20% or the term at several centuries, there is almost always a unit error in the time.

Conclusion

Four formulas solve every simple interest problem. What matters is converting time correctly and rearranging cleanly. The derivation of the formulas is explained in simple interest explained. For percentage problems without a time component, try the percentage calculator.

Simple Interest: 6 Exercises with Solutions