“Compound Interest is the 8th wonder of the world. He who understands it, earns it; he who doesn’t, pays it “- said Albert Einstein. We all would have at some stage in our schools learnt the basic math of calculating Simple and Compound Interest. Albert Einstein has defined the power of compounding as the Eighth Wonder. To be in the category of receiving side of this eighth wonder, we need to know more about the magical Power of Compounding, and the factors that influence it, with greater clarity.
What is Compounding ?
Compound interest makes money grow at a faster rate than simple interest. Because in addition to earning returns on the money you invest, you also earn interest on those returns at the end of every compounding period. For eg I lend someone Rs 100 at 10% simple annual interest. The Principle amount is Rs 100, the rate is 10% and the period can be N years. The simple interest for each year will be constant ie 100 *0.10 = 10. The total interest after N periods will be 10*N. This means after one year it will be 10, after two years 20, and so on.
However, in the case of Compounding interest, the Interest that we earn over a period is merged with the Principal amount. Implying that the interest earned in any period also earns interest in the subsequent periods. In the above eg, the interest after one period would be same as simple interest ie Rs 10. But in the next period, the interest will be on (100+10)*0.10=11. In the third period, it will be (100+10+11)*0.1=12.1 and so on. We can see that the interest earned in the third period is about 21% more than the interest earned in the first period.
Factors Affecting the Power of Compounding
There are three operators at play which influence the compound interest. These are the number of compounding periods i.e. “Time“, the size of principal “Amount“, and the “Rate” at which it is compounding. The relationship is positive in all cases. Which means that the effect on compounding is magnified with increase in either of the factors.
Effect of Time on Compounding
Time is the biggest contributor in compounding. This is also the most important factor on which we can exercise control. There are two elements to time. One is duration which affects the compounding, and other the specific time in the life cycle of the investor. And the good part is that we can exercise reasonable control on both of these. The duration of investment needs patience and we only need to hold on to it for as long as possible.
The timing part is more important, and involves the financial behavior and psychology of the individual. One can invest only when one starts earning, and has surplus money left after catering for his/her living expenses. Subsequently the investor is investing to grow wealth over time to meet some financial objectives. The duration also gets aligned to the financial plan. Boxed between these time frames i.e. the earliest time when adequate money to invest is available, and the latest time when money is required for the intended purpose, one has the option to start as early as possible. Starting early will help extract maximum benefit from the power of compounding.
Effect of Principal Amount on Compounding
There is an old saying that “ Money begets Money”. We can apply it in the context of compounding also. As evident from the mathematical calculations, the quantum of interest earned at a given rate is directly proportional to the principal amount. If this amount is more, the interest earned is more, and the subsequent compounding is more. It is therefore not difficult to deduce that the investor should strive to invest the maximum amount possible, to magnify the effects of power of compounding.
Effect of Rate on the Power of Compounding
Rate of compounding is generally not in the control of the investors. The rate of return provided by different financial instruments post tax is however different. And the choice of right instrument is certainly under our control. Also note that when we talk about rate, it does not necessarily mean interest, but the rate of returns from the investment. While the return from Debt instruments is fairly reliable and predictable, the return from equity is volatile and not assured.
The Combined Effect
When the independent effect of each factor is so evident, it is obvious that the combined effect is also very pronounced. We need to view this effect for two purposes; one, to enhance the power of compounding; and two, to balance the adverse effect, if any, of any of the factors. For eg if the rate of return falls, as is evident by continuously falling rates of interest, our financial plans would need continuous calibration. The fall in rate of return can be balanced by increasing the amount of investment. Or, by switching to another instrument with higher expected rate of return.
Scenario Analysis
The logical deductions seem to be fairly reasonable. However, it might make more sense to measure the influence of these factors with examples, and evaluate the power of compounding.
Scenario 1-Early Investment
Let us take example of a Person A, who starts investing an annual sum of Rs 10,000/- in the year 2000 at 8% rate of return, and stops after 10 years, but does not withdraw the corpus. Another person B starts investing double the amount ie Rs 20,000/- after 10 years ie from 2010 onwards. Both A and B have subscribed for ten years only in this 20-year period. And B has subscribed double the amount. It can be seen from the graph below that the amount after 20 years in the case of person A is still more as compared to B. This is despite B investing double the amount.
Scenario 2-Higher Rate
Let us look at another example when Person A invests Rs 10,000/- every year starting yr 2000 at 8%. And person B invests Rs 10,000/- every year at 12%. We compare the corpus after 20 years. The ending balance in case of higher rate of return is significantly higher as compared to the lower rate of return.
Scenario 3- Increasing Amount
Let us see another example where Person A is investing Rs 10,000/- each year at 8 % in year 2000. And he keeps investing the same amount for next 20 years. Person B also starts with an investment of Rs 10,000/- every year at 8%, but increases this amount by 10% every year. If we see the ending corpus after 10 years, the difference is more than double.
It is now fairly evident that the micromanagement of various factors which influence the power of compounding can yield different results. The various permutations and combinations would of course depend on the possibilities that any individual can explore in his/her own context. The results of different scenarios would also be proportionately different as can be seen in the graph below.
Recommendations
(a) Start investing as early as possible and stay invested till as late as possible.
(b) Invest to the maximum amount feasible and explore the possibility of increasing the investments every year.
(c) Invest in diversified instruments balancing risk and return, so as to optimize the overall portfolio returns.