Calculate a Percentage Sequence

Calculator for a sequence, where with each step a percentual value is added or subtracted. Beginning with a start value, for a given amount of steps the percentual ratio of the current value is counted up or down.

Example: Starting with a value of 100, to which five percent is added in ten increments, the final amount is 162.889. This type of calculation is typical for compound interest, where the accrued interest is further compounded. This calculator can therefore be used to determine the final result of a fixed interest rate on a sum of money. This can apply to investments, where the result is positive, or to loans, where the result is often interpreted as negative. Whether you enter a negative value with minus sign or not is irrelevant, as long as you interpret the result correctly.

Calculating the percentage sequence is relatively simple. The percentage of the initial value is determined and added to it. The process continues in the same way with the new value, and then again, according to the number of steps. This is therefore an iteration. For the example above, the input is z+(5/100)*z, with the initial value z₀=100 and 10 steps. The value for z₁₀ represents the final result. The last value under the summation symbol Σ is irrelevant here.
There is a way to calculate the final result directly without considering the previous individual steps. This uses the compound interest formula, which is K_a=K₀*(1+p/100)^a, where K₀ is the initial capital, a is the number of years, and p is the percentage interest rate. However, if you want to know the individual intermediate results or get a feeling for the development, listing the individual results is of course helpful.