compounding effect Understanding Compounded Returns with Formulas and Examples

The concept of compounded return is related to that of compound interest. As with two sides of a coin, the difference between return and interest can be understood when explained in terms of borrowing money or investing it as an asset. Understanding interest, therefore, makes it easier for us to understand returns.

In this section, you will be introduced to ways of measuring the return of your investment which depend on the time period of said investment.

For investments with a timeline of under twelve months, use the absolute method to measure gains. Conversely, if you’re looking at a longer-term investment, then CAGR or the Compounded Annual Growth Rate is the way to go.

Let’s look at an example to illustrate the difference between absolute and CAGR.

If you invested Rs.100,000/- in a financial asset in 2019 which provided a 10% return annually, how much would you earn after withdrawing it on the first of Jan 2020?

It’s straightforward, as expected.

You will make Rs. 10,000/-, representing 10% of 100,000, from your investment over a period of one year. This is your absolute return for the 365 days considered.

What if we kept the same investment over three years instead of a single year and compounded the 10% return on an annual basis? How much would you earn at the end of the term?

We can work out this figure by utilizing the growth rate formula.

Amount = Principal*(1+return)^(time)

This formula is also used to calculate compound interest. Applying this same equation produces the desired result.

100,000*(1+10%)^(3)

= Rs.133,100/-

As was mentioned in the preceding section, charging compound interest results in the same amount of interest you would receive from your friend in the third year.

Moving onward, let’s consider another query –

If you put Rs.100,000/- into an investment and after 3 years you’ve earned Rs.133,100/-, what is the rate of return?

To answer this query, all we must do is rearrange this equation.

Amount = Principal*(1+return)^(time)

and solve for ‘return’.

The formula is then transformed to –

Return = [(Amount/Principal)^(1/time)] – 1

Return here is the growth rate or the CAGR.

Using this approach to tackle the issue –

CAGR = [(133100/100000)^(1/3)]-1

= 10%

The compounding effect

Albert Einstein apparently labelled ‘compound interest’ as the 8th wonder of the world – a phrase that accurately conveys its power. To truly grasp its marvels, it must be studied in conjunction with time.

Compounding in finance can lead to money increasing dramatically over time due to reinvesting gains from one year to the next. By repeating this process, there is potential for enormous growth.

If you invest Rs.100 expecting annual growth of 20%, this is known as the CAGR of growth rate. After one year, your money will be worth Rs.120.

At the conclusion of year 1, you have two choices –

Keep Rs.20 in profits with the initial capital of Rs.100

Take out a profit of Rs.20

Instead of withdrawing Rs.20 as profit, you opt to reinvest it for a second year. After the passage of 12 months, Rs.120 has grown to Rs.144 due to a 20% increase in value. Subsequently, this final figure is itself subject to a 20% growth over the following year, resulting in an overall total of Rs.173 at the completion of 3 years. And this cycle will continue similarly with the invested capital.

Rather than withdrawing Rs.20 year after year, you would’ve accumulated Rs.60 in just three years’ time.

Having decided to stay invested, you were rewarded with Rs.173 profits after 3 years – a 21.7% increase from the Rs.60 that would have been earned had you done nothing.

The compounding effect occurs when a small increase or decrease over time adds up to a larger change. This is an accumulative phenomenon.

Let’s explore this further by examining the chart below.

A visualisation of how Rs.100, if invested at 20%, would grow over the course of 10 years is demonstrated via the graph above.