# How does this calculation work

## How does the mixed interest work?

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The mixed interest combines the simple interest with the compound interest calculation.

If a non-whole number of years is specified as the term, the interest calculator uses the mixed interest rate.

### Compound interest calculation for whole years

For a whole number of years, the interest calculator calculates from start to finish **compound interest**, provided compound interest calculation on the setting *Yes, interest accrual* was chosen.

One year is set as the interest period for the interest calculator. It is assumed that interest is credited once a year, always at the end of the year. With an investment period of two or more (full) years, the interest calculator calculates compound interest from the second year onwards. Interest credits from all previous years are also subject to interest. One speaks of annual compound interest.

Example: For a one-off investment capital of 5,000 euros, with an annual nominal interest rate of 4 percent, 200 euros interest at the end of the first year. These are credited to the investment capital. At the end of the first year, the investment capital had grown to 5,200 euros. At the end of the second year, this capital (with the same nominal interest rate) is already earning EUR 208 interest. Interest from the first year was also compounded. The new interest is also credited back to the investment capital. The credit at the end of the second year is therefore 5,408 euros.

Mathematically, this results from raising the interest factor 1.04 to the exponent 2. The interest factor stands for the interest (1.04 means 100 percent of the capital, plus 4 percent interest). The exponent stands for the number of years. In formula notation:

5,000 euros * 1.04^{2} = 5,408 euros

### Simple interest with a pro rata interest period

What would happen if the term was only half a year? Here is the **simple interest** applied, provided that the bank's customary linear interest rate has been set for the period during the year.

In the example above, the interest for the entire first year would be 200 euros. However, if the capital is only invested for half a year, only half the interest income will result. In this example, the interest income for half a year is 100 euros. At the time the interest is credited, the credit would therefore amount to 5,100 euros.

As a formula, this can be represented as follows:

5,000 euros * (1 + 0.04 * 0.5) = 5,100 euros

You can see immediately that this formula differs from the formula above. If you would just replace the exponent in the above formula, i.e. 1.04^{0,5} instead of 1.04^{2} arithmetic, one would arrive at a wrong result. This is because the above formula is based on an exponential rate of return, even if the year is proportionate. In practice, however, this is usually not the case, so simple interest can be expected here.

### Mixed interest

If the final balance is now to be calculated for a term of 2.5 years, a combination of compound interest calculation and simple interest is carried out, which is used as **mixed interest** referred to as. Both calculation methods are used one after the other:

This results in a credit of 5,408 euros again after the second year. For the remaining six months it then follows:

5,408 euros * (1 + 0.04 * 0.5) = 5,516.16 euros

The final credit after a 2.5-year term with mixed interest at the time of the interest credit is therefore EUR 5,516.16.

### Check yourself

To understand the example itself on the interest calculator, here are the input values:

- Mark which value is to be calculated: Select Calculate final capital
- Enter the given values as follows:
**Initial Capital:**5,000 euros**Interest rate:**4.0% p.a.**Running time:**2.5 years**Final capital:**- set free -**Compound interest:**Yes, select interest accrual**Tax rate:**- do not take into account -

Call up in the interest calculator

Note that the credit history table (at the bottom of the interest calculator page) for *three* Years. This is because the interest credit for the last six months of the 2.5-year term is not paid until the end of the third year.

In practice, in this example, the existing credit would be paid out after 2.5 years. At the end of the third year, you would finally receive the interest credit for the last six months, since it was assumed that the interest credit is only ever made annually at the end of the year.

Read on: Different interest rates every year

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