# Interest calculation

## Interest terms

Initial asset

K0 (asset after 0 Interest Periods)

Final asset

Kn (asset after n Interest Periods)

Runtime

n Number of interest periods

Interest rate

p per interest period

## Interest Calculation

Interest calculation includes calculation procedures for interest on borrowed capital. E.g. in the form of loans or savings deposits. The interest is calculated in fixed periods, e.g. annually. I.e. a savings deposit is credited annually with an interest amount. The interest calculation gives formulas to calculate the capital development depending on interest rate, term and initial capital. A distinction is made between linear and exponential interest depending on whether the interest is also interest-bearing or not.

### Linear interest rate

To calculate interest for a given period with an equal interest rate, the general interest formula applies:

${K}_{n}={K}_{0}\left(1+\frac{p}{100}n\right)$

The interest formula indicates the final capital after n interest periods. If the interest is paid annually, n corresponds to the number of years. I.e. the initial capital is interest-bearing n times and the final capital is the sum of initial capital and interest. The interest is not calculated here.

The time (in interest periods) until the invested capital doubles can be calculated, depending on the interest rate, using the formula for capital doubling:

${n}_{T}=\frac{100}{p}$

After nT interest periods, the invested capital has doubled.

### Example for linear interest calculation

1000€ is invested for 10 years with 5 percent interest. This results in a final capital of 1500€.

${K}_{n}={K}_{0}\left(1+\frac{p}{100}n\right)=1000\left(1+\frac{5}{100}10\right)=1500$

In the example, the initial capital doubles after 20 years.

${n}_{T}=\frac{100}{p}=\frac{100}{5}=20$

### Compound interest (exponential interest)

In compound interest, the interest of the previous periods is added to the interest of the following interest periods. I.e. the interest income is added to the capital on which interest is to be paid. The compound interest formula mathematically represents an exponential function. Generally described by f(x) = ex. The exponential function also describes growth processes in nature (e.g. the multiplication of bacteria).

${K}_{n}={K}_{0}{\left(1+\frac{p}{100}\right)}^{n}$

The compound interest formula indicates the final capital after n interest periods. If the interest is calculated annually, n corresponds to the number of years. In this case, the interest is added to the fixed capital and interest is added in the subsequent periods.

The time (in interest periods) until the invested capital doubles can be calculated, depending on the interest rate, using the formula for capital doubling in the case of the interest rate:

${n}_{T}=\frac{\mathrm{log}2}{\mathrm{log}\left(1+\frac{p}{100}\right)}$

After nT interest periods, the invested capital has doubled.

### Example of exponential interest

1000€ is invested for 10 years with 5 percent interest and reinvestment of interest. This gives a final capital of 1628.89€.

${K}_{n}={K}_{0}{\left(1+\frac{p}{100}\right)}^{n}=1000{\left(1+\frac{5}{100}\right)}^{10}=1628.89$

In the example, the initial capital doubles after 14.2 years. With linear interest in the first example, the initial capital doubles only after 20 years.

${n}_{T}=\frac{\mathrm{log}2}{\mathrm{log}\left(1+\frac{p}{100}\right)}=\frac{\mathrm{log}2}{\mathrm{log}\left(1+\frac{5}{100}\right)}=14.2$

### Interest calculator for interest and compound interest

The interest calculator for interest and compound interest calculates the capital development for interest and for reinvestment of interest. Enter the initial capital, the number of interest periods and the interest rate. In the case of annual interest, the interest periods correspond to the term in years. The result is displayed graphically and in tabular form.

Interest periods

n=

Initial capital

K0=

Interest rate

p=

%

Scale:
Points interest:
Points compound interest:

Calculated values for the capital according to the interest and compound interest formula:

### Screenshot of the Image

Print or save the image via right mouse click.

## More Calculators

Here is a list of of further useful calculators:

Index Fraction calculator Percentage calculation Per mille calculation Rule of three calculation Conversion of number systems