On Compounding Frequency (again)

By Moez Sghaier

April 4, 2024 6:36 p.m.

It looks like a textbook case, right? Yes it is. The more you increase the frequency of compounding, the more your investment’s value increases. This happens by including the earned interest/return into the invested capital. So, the more you keep the interest/return invested, the more you increase the invested capital and the more you get rewarded for doing it.

Demonstration

Let’s demonstrate how a shorter period of compounding is more beneficial for the investor than a longer one. To do so, we need to introduce a few concepts including the effective rate of interest/return, f. According to financial/business mathematics,

f = (1 +i)(power m) -1 where:

f = effective rate of interest/return

i = periodic interest rate, i = j/m

j = nominal annual interest rate

m = number of compoundings per year

As an example, let’s take a nominal interest/return rate of 5% per year, i.e. j = 5% or 0.05.

Then, let’s fill in the table below to show how the effective rate of interest/return increases when the period of incorporating interest/return into the capital increases within the year.

Period	Half a year	Quarter	Month	Two weeks	One week
j (%)	5	5	5	5	5
m	2	4	12	26	52
i (%)	2.5	1.25	0.416666667	0.192307692	0.096153846
f (%)	5.0625	5.0945	5.1162	5.1221	5.1246
FV ($)	1050.63	1050.95	1051.16	1051.22	1051.25

The last row in the table shows the value of $1,000 invested at different compounding frequencies within the year. According to financial/business mathematics again, the future value, FV of an amount of $1,000 invested today i.e., the present value, PV is given by the formula:

FV = PV (1 +i)(power m) when considering one year of investing only.

Once again, we see that the future value of our initial investment of $1,000 increases with the compounding frequency.

One can argue, however, that the increase is minimal, a few cents to a dollar, in the example above but when the amount invested becomes thousands of thousands of dollars over many and many years, the investor should be able to witness the time value of money and benefit from the magic of compounding frequency.

Advice

So, my advice to you today is to first start investing any non-essential cash you have, and second do it in a smart way by choosing the highest frequency possible within the year, i.e. putting aside an amount weekly is better than bi-weekly which is better than monthly which is better than quarterly, and so on. You got the point, right?