The following is an extract from MYFE Book 1
The Inevitable Maths of Compounding
We all think we understand what compounding means, but do we?
Compounding has become used in the vernacular to describe many things. If you want to lose weight, eat less and exercise – the effects will compound. If you want to learn something, read lots of books and your knowledge will compound. If you want to sustain a relationship, make time and invest in the other person – the benefits will compound, etc…
It’s the same with investing, except it’s easier! With investing, compounding doesn’t ask anything of you – just to leave it alone to get on with its job (see Table 2 below).
But what exactly is compounding? Compounding is an exponential calculation, such that interest or investment returns get added to interest/returns, which gets added to interest/returns, until it takes on a life of its own and snowballs, gathering mass and speed all the time you don’t touch it, i.e. don’t withdraw your investments.
Being an exponential calculation, we struggle to calculate the value of compounding after just a few iterations. And because we can’t do the maths in our heads we’re inclined to forget about its effect on our savings and investments. Please don’t do that.
Compounding is not a miracle, it’s an inevitable mathematical fact. Simple interest is calculated on the principal invested each year. Whereas compound interest is calculated on the principal plus the previous year’s interest. In short…
Simple Interest = Interest on Principal
Compound Interest = Interest on Principal & Accumulated Interest
Table 2 illustrates the difference between simple interest (the one we reflexively calculate in our heads) and compound interest (the exponential calculation we can’t do in our heads). The investor in this example doesn’t invest an additional £5,000 every year, they just let their initial £5,000 in year one roll over each and every year.
You will also note from Table 2 how interest earned each year grows and accelerates with time, thanks to compounding. This is one of the key reasons I suggest you start investing as soon as you can. Having invested £5,000 in the example for Table 2, the difference between simple interest and compound interest is £20,200.
Finally, and just to reinforce the importance of compounding’s relationship to time, Figures 4 and 5 illustrate that relationship, and how giving compounding time significantly accelerates your returns.
Interestingly, based on Figure 4, in order to match Jill’s final returns, Dave would have to invest £213 per month from age 35, while Robyn would have to invest £487 per month from age 45. If all three of them had invested £250 per month at the start, instead of £100 over the same periods, Jill, Dave and Robyn would have final returns of £765,366, £359,186 and £157,072, respectively.
Figure 5 is the same data as in figure 4 but expressed visually in a different way. The reason for including it here is to emphasise how by starting earlier, compounding has exploded Jill’s returns.
If you use an online calculator to establish how the numbers in Figures 4 and 5 are derived, please note the numbers are compounded monthly, not yearly. This more accurately reflects the outcomes for Jill, Dave and Robyn who drip-feed their savings into their investments on a monthly basis.
For those of you who like a blended learning experience, here’s an excellent vlog by Dave Ramsey (bit.ly/3ipt7ec) that makes numerous compelling points while demonstrating the power of compounding.
Takeaway
The key to the magic of compounding is time.