### CAGR calculator

The CAGR Calculator (Compound annual growth rate) would tell you how much annual returns an investment made over a number of periods. This can be used for one-time investments like a real-estate investment or a lump-sum investment.

##### Disclaimer:

Results shown for illustrative purpose only and should not be construed as investment advice.

## What is CAGR

(also known as compound returns, compounded annual returns, Annualized returns)

Mutual fund investments are often, and rightly so, made for the long-term. And by long-term I mean a time period lasting several years. In such a situation, it would be very useful to look at how much a fund returned (or “performed”) on an annual basis rather than on an absolute basis.

There are two important reasons why this is so:

1. Time matters: If we want to know whether an investment return is ‘good’ or ‘bad’ we need to know how long it took for the return to materialize. Many other financial metrics, especially inflation, are expressed in annual terms, and for us to benchmark our returns with these other metrics, we should use something that is correlated with time as well.
2. Making things comparable: We are faced with plenty of investment choices, and not just in mutual funds. To be able to make a decision, we need to be able to compare these instruments. And for that, we need a metric that we can use for comparison. The earlier metric that we saw – the absolute returns – is absolutely useless in this regard. Why? Because you could say your instrument returned 40% and I could say mine returned 60%. But yours could have happened over 2 years, and mine over 10. Unless we express these numbers annually, we cannot compare them fairly.

### What is annual return

Simply put, annual returns are absolute returns annualized. What does that mean? It means expressing a return in such a way that the return builds on itself (compounds) every year. That is why these are also called compounded annual returns or compounded annual growth rate (CAGR – although technically, it need not always be growth since CAGR can be negative as well).

The formula for calculating annual returns on an investment is to simply take the return fraction and raise it to the power of (1/n) where n is the number of years invested (and then subtract 1 to remove the principal component). You don’t need to “understand” this formula – just knowing that there is one is enough – you can always look it up!

This is just the formula. Things will get a lot clearer when we look at an example.

### Example

Let’s first understand the arithmetic aspect of compounding with a simple non-mutual-fund example. Suppose you lend me Rs 1 lakh and I offer you 10% interest on it for a year. At the end of the year, I would give your Rs 1.1 lakh (Rs 1 lakh + 10% of Rs 1 lakh = Rs 1,10,000). Now, if you lend me back the Rs 1.1 lakh and I offer you 10% interest again, at the end of the second year, you make Rs 1.21 lakh (Rs 1.1 lakh + 10% of Rs 1.1 lakh = Rs 1,21,000). Money building on itself in this manner is what is called compounding.

However, if you give me money for 5 years, and I tell you I will give you double the money after 5 years – the total returns (absolute return) you would make on your investment – over 5 years, mind you – would be 100%.

Now, what would I tell you if you ask me what the “annual returns” are? Should I say that it is 20% (100 divided by 5)? Well, that would be what’s called the ‘simple returns’. There’s nothing wrong with specifying that, but in the world of finances, the traditional way is to represent the annual returns in the form of compounded values.

(Why is that so? Because invested money grows on itself – that is a fundamental principle of investment. If you start a business with Rs 1 lakh and you make a profit of Rs 20,000 in a year, you deploy Rs 1.2 lakh in the business the second year so you can make a profit of Rs 24,000 in the second year, and so on. The most accurate way of capturing this growth is by using compounding)

So, let’s get back to our scenario. The annual returns on the amount lent to me (Rs 1 lakh set to double in 5 years – absolute return of 100%) would be, applying the formula above:

CAGR = (Rs 2 lakh/Rs 1 lakh ) to the power of 1 over 5, minus 1.

And that would be equal to 14.87%

What this means is that the money compounded every year at the rate of 14.87%.

Let’s verify that:

Rs 1 lakh @ 14.87% growth at the end of one year would be 1,14,870.

Now, since we are compounding, we apply 14.87% on Rs 1,14,870 for the second year. So, at the end of second year (thanks to my calculator) would be Rs 1,31, 951. Going forward, the same calculation would give us Rs 1,51,572 at the end of 3rd year, Rs 1,74,111 after 4 years, and Rs 2,00,001 at the end of the fifth year. Voila! Double in five years!

So, this is  how CAGR gets “calculated” from an absolute return. CAGR can be used to represent returns in the past (how much a fund gave in the last five years), and for the future (how much will a deposit – not a fund – will give in the next x years).

(Please note that some bank deposits offer quarterly or half-yearly compounding of interest as well – I am not covering those scenarios here since my focus is on mutual fund returns, and also because in most cases that’s just a marketing gimmick

Let’s look at the right and wrong use cases of CAGR now.

### How it should and should not be used

Annual returns are a versatile metric – it can be used in many useful ways. However, there are also situations where it would simply be wrong to use them to represent returns. Let’s look at them in turn.

The best use case for annual returns would be to compare two similar investment instruments. If you go to one bank and they offer you 8% interest for a 3-year term deposit, and you to another and they offer you 8.5% for the same term, it would be fair to compare these numbers. Similarly, when you look at past performances of mutual funds, if you look at two similar funds and their track record over similar time frames, annual returns would be the right metric to use.

However, you should keep the following in mind:

1. You should not use annual returns for any period less than one year. We saw this in the earlier section as well, and it bears repeating. If someone tells you a scheme returned an annualized 8% in the last 6 months, it means it returned 4% in the last six months. And nobody knows what will happen in the next six months. So, annual returns should not be used in this context.
2. You should not compare returns over different periods in time. If a fund returned x% annually over a 3-year period and another fund returned y% over a 1-year period, x and y are not comparable.
3. When it comes to mutual funds, past returns are always expressed as annual returns. However, this says NOTHING about what the fund will return in future. As simple as this sounds, I just want to state it for the record.
4. Annual returns cannot and should not be used for SIPs. More on that in the next section.
5. Annual returns (in this form) cannot be used to calculate how much your investment returned when your investment involves multiple transactions.

When you look at mutual fund factsheets or website displays, you will find a lot of performance numbers. Most of them show absolute returns for period less than 1 year and annual returns for period greater than 1 year. Understanding and internalizing the concept of compounded annual returns is very important for interpreting those numbers correctly.