Calculate the Mean Value for Compound Interest

Calculator for the average interest rate for variable interest rates over a longer period. The interest rate can change and does so frequently over a longer period. Here it is assumed that the interest rate always applies for a full year or integer multiples thereof. If the change occurs regularly every few years, then the entry can also be for this longer period. Otherwise, the interest rate must be entered separately for each year. Please enter the interest rate in the form of, for example, 2 3 4 for 2, 3, and 4 percent. If 3 percent is paid over two years, the input would be as follows: 2 3 3 4.
Please enter the different interest rates one after the other, separated by spaces or ;. The mean will be calculated.

In compound interest, the average of the interest rates is not the familiar arithmetic mean, but the geometric mean. Here, the individual n values are multiplied together and then the nth root is taken. The geometric mean is always smaller than the arithmetic mean (or equal if all n values are identical, but then you don't need a calculator). This isn't done to defraud savers; it's a mathematical necessity; it simply corresponds to correct calculations using exponential functions.

The calculation works as follows: First, the interest rates are converted into factors, for example, 2 percent into 1.02, 3 percent into 1.03, and so on. This also allows calculations with negative interest rates. Then, all n factors are multiplied together, and the nth root is taken from the result. The result then has the form of one point something. The one is subtracted, and the decimal part is multiplied by 100 to return to the percentage.
The formula is: x_geom = ( Π(1+x_i/100)^1/n - 1 ) * 100
with the product function Π from i=1 to n and the single interest rates x_i.