~The first two are extremely popular in the business world, while the last is used occasionally. Let's take a closer look at all of these & how they are calculated.

 

~Percent Increase: If we quantify an item (measure or place a numerical value on it) and this value increases, the percent increase is often used in this scenario. For example, if the price of a stock selling at $20 a share goes to $24 on a give day, the $4 increase is usually stated as a percent increase in the investment world.

 

~To find this percentage increase we need to take the amount of increase (4) and divide it by the starting point value (20). This gives a decimal. We then convert this decimal to a percent. For the above example, we have 4/20 = .20 = 20 % increase. This would be considered a large increase in the investment world, since, now-a-days, placing $20 in a savings account for one year would increase to $20.40 at an interest rate of 2% (if you are lucky).

 

~The key to figuring correctly is the starting point. For increases, the starting point is lower than the end point. However, for decreases, it's higher. Let's take a closer look at that case.

 

~Percent decrease:  If your $20 stock went down instead of up, we would have a decrease. Let's say it fell to $16 on a given day. That is a decrease of $4. The starting point is the same as the first example, so, place the decrease of 4 over 20 to get .20 = 20 % decrease in price. Now your stock is at $16 and you are very unhappy. You would like your original money invested back (less commissions). What percentage increase must occur for the stock to get back to the original price of $20?

 

~Be careful here, since the starting point is now $16 and needs an increase of $4. So, placing the increase over the starting point, we have, 4/16 = .25 = 25%. So, a 20% loss followed by a 20% gain will not get you back to the original price. The reason for this is the fact that percentages are based on the starting points. The lower the starting point the higher percentage necessary. A bit tricky for the novice investor.

 

~In the investment world, percent increases & decreases are used extensively. In the stock market, a stock is followed second by second & these increases or decreases are usually displayed next to it's price. Now for a more advanced type of increase or decrease.

 

~Percent rate of change:  A little calculus is needed here to understand rate of change. When this phrase is used, it means instantaneous rate of change. That means the rate of increase or decrease of the quantity in question at an instant (or point on it's graph).

 

~For a linear function (straight line curve), no calculus is needed, this rate of change at a point is nothing more than the slope of the straight line function. Since the slope of a linear function is constant (the same at every point), all you have to do is find the slope of the line.

 

~However, for a non-linear curve (graph is not a straight line), the slopes vary from point to point. In calculus, we find these slopes by means of the derivative of the function at the point in question. This is nothing more than the slope of the tangent line drawn to the curve at that point. Now for the percent rate of change.

 

~To find the percent rate of change, simply find the rate of change at a point and place it over the value of the function at that point (y-value at that point). Then covert this decimal to a percentage. That's it! The following is a simple example using a linear function.

 

~Find the percent rate of change for the linear function y=3x+4 at the point where x=2.

Since this is a linear function, the rate of change is the same at all points on the curve. It's the slope of the line. From basic math, this is 3.  At x=2, the value of the function is 10.

Therefore, we have, 3/10 = 30%. The percent rate of change will be negative for a decreasing curve since the rate of change (slope) is negative.

 

~From my experience, percent rate of change is rarely used in basic levels of business investment, while percent increase or decrease is quite popular.