Compound annual growth rate: Understanding the math of how your money can grow

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CAGR can be used to assess the average annual growth rate of various investments, including stocks, bonds, real estate, cryptocurrencies, and retirement accounts. Photo: Pexels/ Cottonbro

Imagine your money going on a rollercoaster ride in the stock market or any investment. That is the same factor that pulled people into investing in the stock market today. But what they look for is an immediate growth. But getting rich in the stock market is all about the long game, a little bit of luck and a lot of patience. 

In the long run, one can get rich in their investment, stock or otherwise, without doing anything. You just use the power of math and let that bank in the money for you while you focus on your life. In other words, it is the steady growth rate that helps you see the big picture without the financial rollercoaster.

So what is the big secret? It is all about Compound Annual Growth Rate or CAGR.

Technically, CAGR is a measure used to determine the annual growth rate of an investment over a specified period, assuming that the investment has been compounding over that period. It provides a smoothed annual rate of growth, taking into account the effects of compounding.

In any moment of confusion about different investment options, it is like the much-needed sense of which investment is worth pursuing in the long run. CAGR can be used to assess the average annual growth rate of various investments, including stocks, bonds, real estate, cryptocurrencies, and retirement accounts.

How to calculate CAGR

The formula for calculating CAGR is:

In the formula:

Ending Value or EV represents the ending value of the investment or asset. 

Beginning Value or BV represents the beginning value of the investment or asset.

N represents the number of years.

Assuming an initial investment of Rs 1,000,000 and an end value of 3,000,000 (rounded off), we’ll calculate the CAGR after 15 years.

So, the Compound Annual Growth Rate (CAGR) for this investment, with an initial value of Rs 1,000,000 and an ending value of Rs 3,000,000 over 15 years, is approximately 7.7 per cent. 

Analysing the end game

But you want to find out the end value or how much you will acquire from your initial investment. So the formula to use here would be: 

Here, assuming an initial investment of Rs 1,000,000 and a CAGR of 5 per cent, we will calculate the Ending Value after 15 years.

Therefore, assuming there is an annual growth rate of 5 per cent, the future value of a Rs 1,000,000 investment after 15 years would be approximately Rs 2,078,928. 

Power of compounding 

You might be asking why use CAGR in the first place. The interest rates given by your current banks are enough. Because they calculate the return in simple interest. 

Your savings and fixed deposits are of course not bad, they are your safest bets and you should have them and diversify your assets. But the difference does lie in the results. So in comparison, for your savings and fixed deposits, the total amount you earn at the end is calculated like this:

Earnings = 1,000,000+(1,000,000×5×15)

Earnings  = Rs 1,750,000

Considering that the average interest rates, given by the Nepali banks, in the savings and fixed deposits are 6 per cent and 9 per cent respectively. 

Here is what you would earn in a year for the same.

SavingsFixed Deposit
Rs 1000000+(1000000×6×1)1000000+(1000000×9×1)
Rs 1,060,000Rs 1,090,000

And, at the same rate, this is your earnings in 15 years (simple vs compound):

SimpleCompound Earnings
1,000,000+(1,000,000×6×15)1,000,000×(1+ 6/100)15
Rs 1,900,000Rs 2,350,000


Fixed Deposit
SimpleCompound Earnings
1,000,000+(1,000,000×9×15)1,000,000×(1+ 9/100)15
Rs 2,282,764.24Rs 3,472,697.81

You can see the difference in just two years.

For Rs 1,000,000 with a 5 per cent interest rate for 2 years, the total earnings (principal and the interest) would be: 

Simple Interest = Rs 1,100,000

Compound Interest = Rs 1,102,500

Key takeaways:

So why is Compound Annual Growth Rate (CAGR) preferred?

CAGR represents the overall growth rate of an investment, considering both positive and negative fluctuations. It provides a holistic view of how an investment has performed over time. It is often used for investments with market exposure, and the returns can be influenced by market conditions.

As it provides a smoothed annual growth rate, mitigating the impact of volatility and short-term fluctuations in investments, there is a more stable and realistic assessment of performance over time, with a standardised metric.

It applies to a wide range of investments where the value can fluctuate over time, especially in market-driven assets. It’s commonly used in finance and investing to evaluate the performance of investments such as stocks, mutual funds, and portfolios. For that, understanding CAGR becomes indispensable for making informed decisions.

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