Additional Information
This dual-purpose calculator is designed to deal with those cases where something is growing (or shrinking) at a steady rate.
Different words are used for these. Growth is also known as 'appreciation' when it is said that something has appreciated in value, meaning that its value has increased. The opposite case of shrinking, or growing smaller, is referred to as 'depreciation' when talking of something whose value has decreased, though in science the word 'decay' is also used.
(Mathematically, both can be put together as growth, by keeping in mind that growth can be positive or negative.)
Basic to all of this is the idea that the change, expressed as a percentage, is taking place at regular intervals (periods). But it is a matter of HOW that change is applied which distinguishes between simple and compound growth.
Simple growth (or decay) means that the same amount is added to (or taken from) the changing value at the end of each period. And that 'same amount' is the percentage of the start value.
Compound growth (or decay) means a different amount is added to (or taken from) the changing value at the end of each period. This amount has to be re-calculated as the percentage of the changing value at that time.
For instance consider a start value of 200 at 5%
Under simple growth 5% of 200 (=10) has to be added on each period so the changing values go200, 210, 220, 230, 240, 250, etc.Under compound growth the beginning looks the same200, 210 but the next value has to be found by adding on 5% of 210 (not 200) and that is 10.50 to give 200, 210, 220.50
At end of next period 5% of 220.50 must be added on (=11.025) and this process continued so the sequence of changing values becomes200, 210, 220.50; 231.53; 243.10; 255.26; etc All having been rounded to 2 decimal places (currency values).
|
|
Format and Limits
As far as possible, the output values are given in the form of currency (that is, to 2 decimal places) and with spaces between each group of 3 digits, to make them as readable as possible.
However, the compounded values can become very big (and very small). In order to fit them in, the first thing to go is the spacing. Next, they are given in e-Format, and when they grow beyond that, there is a note that they are out of bounds. Remember that compounded values must exist and must be positive (they cannot be zero or negative) but their size can make it impossible for the program to handle them. We are talking here about numbers which are in excess of 200 digits long.
There is a separate note on the e-Format, if needed, to be found underFormat and AccuracyOnly one of the output values can ever be negative. That is the one for simple decay. Whether that negative value has any real meaning or not can only be decided by the context of the situation. It might be meaningless, or it might represent a debt. The input values have limits placed on them.- Zeros and negative values are not accepted.
- The start value cannot be less than 1
- The start value cannot be bigger than 1 billion.
- The rate of change cannot be more than 100 %
- The number of periods cannot be more than 1000
These values are of no particular significance, but some limits had to be set, and these should cover all 'ordinary' needs. |