power of compounding


Kisan Vikas Patra, the original claimant to “Double Your Money” marketing campaign has been with us since decades. As a kid, the math behind it intrigued me. It was the Power of compounding which I learnt later in middle school, but there was no way to quickly know how many years it would take to double or triple the investment. My mother was the official financial planner of the house, even though father was the sole bread winner, as in the case of millions of middle-class families. Doubling money was one of her cherished goals as she tried to match the cash outflows to current cash balance plus future earnings of my father plus investment earnings. It included both revenue and capital expenditures – like college education and children’s weddings. And the plan was reviewed frequently to adjust for any unforeseen hiccups. That’s cashflow forecasting at its best! MS-Excel – you were not there to help. It was all in her mind and utmost on a few pieces of paper. A simple Casio pocket calculator, which my father used in his hospital to reconcile veterinary drug inventory and his monthly expense statement to the HQs, was all the tech there was. But she was not very fond of it. She took to the traditional path of using pencil and a paper to work it out. But most times it was my father’s and my task to re-compute and re-verify the “return” claim of every investment opportunity.

KVP was part of her investment portfolio. 80s and 90s were the good old days of high interest rates – my earliest memory was KVP promising to double the money in 5 years, which became 6 years by late 80s, then 7 years and so on. Currently it is at around 13 years (After the reading this article try to arrive at the interest rate offered if doubling is promised in 13 years – you can give your answers in the comment section). And that claim was taken at face value without any doubts. Government backed security – so no risk of default. So, if they can double your money in 5 years what is the interest rate they offered? Or if they offered 10% interest per annum – how long it took to double your money. You can arrive at the rate of interest and the years to double by using Compound Interest formula you learnt in your middle school. Both these questions can be answered by applying the knowns in the formula A = P(1+r/100)^n to arrive at the unknowns.  P = Your initial investment or Principal amount, r = rate of interest per annum, n = number of years and A = Maturity amount.

That calculation would take some time, say a few minutes, but if you apply the “72 Thumb rule” – it takes exactly 2 seconds – may be less if you are quick in basic math. It’s a one-step formula – divide the number 72 by the rate of interest per annum to arrive at the number of years it would take to double your money. If your investment is earning 10% per year, then it takes approximately 7 years and few months to double. If interest is 8% – then doubling time is 9 years. And conversely if they claim the investment will double in 6 years you can arrive at interest rate per annum by dividing 72 by 6. The answer would be 12%. It is important to remember the effect of compounding here. That means the interest earned in first year gets added to the principal amount and the interest for the second year is calculated based on initial investment plus first year interest earned. The interest keeps getting added and the compounding chain continues till maturity. And that’s Magic!

Interest Rate Years to double
8.00 9.00
9.00 8.00
10.00 7.20
11.00 6.55
Table with interest rates and years to double

We will continue to learn more tools that are generally used in Corporate world, but equally adaptable to personal finance decisions. If you want us write on any topic of your choice in Finance, Economics, Tax, Medicine – do let us know in the comment section. We will be happy to help.