Compound interest is the eighth wonder of the world is the famous phrase attributed to Albert Einstein. The effect of compound interest is benign in the beginning. As the time goes the effect starts to get significant and the exponential growth that it will produce is amazing. Its is therefore imperative to have the compound interest working for us rather than against us. For example, the initial money of 100 at 5% annual growth will amount to around 128 in 5 years. This means we have more money in our pocket. However, if the initial amount is money that we owe someone then the growth over a period of time will be money out of our pocket which is often unpleasant and hopefully not damaging. Rule of 72 gives a quick estimate of the doubling effect. By dividing 72 by the annual interest, we will get the estimated time the initial amount will double. In the previous example, by dividing 72 by 5 (annual interest) gives approximately 14 years. This 14 years is the time it takes for the initial amount to double. As we can see, the bigger the denominator the faster the doubling time will be. If the annual interest equals 72, it takes just one year to double. When the annual interest surpasses 72 the doubling time will be reduced to less than one year.
This doubling time has wide ranging applications to estimate growth of various units of quantity and it is not necessarily about money only. Doubling time is used to estimate growth of cancer in patients, population growth of nations and extinction of endangered species. Radioisotope half life is doubling time in reverse. This property gives scientists tools to study fossils of rocks & organisms and enables them to date the origin of the species from many many years ago.
Evaluation of maintenance costs on machinery is essential. In fact, this should dictate how we should approach our maintenance on that particular piece of machinery. If we are spending too much money on maintaining a machine perhaps it is cheaper & wiser to run that machine to failure. Probably, this will save money in the long run. How much is spent as a percentage of part replacement indicates the ratio of money spent to maintain against buying new one. This fraction of cost maintaining a machine will grow over long time. Suppose a new machine cost 20,000 to set up and maintaining that machine will cost 1000 annually. This translate into 5% of the replacement value if we are to scrap the machine and get a new one. At 5% annual spending, it takes approximately 14 years (72/5) to get the initial value to buy the machine. If we spend 10% annually, time it takes to get the cost to replace the machine is around 7 years (72/10). Obviously, this calculation is an oversimplification. However, it should give us some perspective on our maintenance approach.