Compound Returns

Darryl Bachmeier
Sep 6, 2020

Compound return is sometimes associated with the term annual average return. The term compound return refers to the annual rate of return earned on the original amount of an investment in a time-period. The calculation is not always accurate but it is better than calculating average returns. Not the actual rate of return. You will understand the meaning of this in the example we will provide shortly. Before that lets take a deeper look into the definition of compound return.

What is compound return?

Compound return is the rate of return earned on a capital over a period of time. It is expressed in percentage. If a capital investment reports to have 5% compound return annually for five years, that means the outcome of that investment will be exactly the amount it would earn if the investment had 5% annual interest rate from the beginning.

Compound return results will give you the correct answer on a cumulative level, but on a detailed level, it may not be correct. You will see that in the example later. Now, let’s see how you calculate compound return.

How to calculate compound return?

For calculating compound return, you first need to calculate the compound annual growth rate (CAGR). The formula of calculating CAGR is,

In the formula, EV = Ending value BV = Beginning value n = year

The answer you will get from it will be in decimal. You need to multiply that answer with 100 to convert it into percentage. We will use that answer of CAGR and use it to calculate compound return. Note that CAGR is not the true rate of growth. It is a representational figure that smoothens the return of each year. It makes investment returns easier to compare with other alternatives.

Example of compound return

Let’s take an example of $1000. Suppose you are spending $1000 as a capital investment. After 5 years, you ended up with $1276.28. We have to calculate the compound return of this investment. Before that we need to calculate its compound annual growth rate (CAGR).

CAGR calculation

We will use this formula. From the given values, our ending value (EV) is 1276.28. Our beginning value (BV) is 1000 and the number of years, n is 5. If we input these three values in the formula and calculate it, we will get a value equal to 0.04999. To keep our calculation simple and easy, we will take 0.05 (near 0.4999). Remember that the answer of CAGR needs to be multiplied with 100 to convert it into a percentage format. So if we multiply 0.05 with 100, it will be 5%. This 5% is our annual rate of return. Now let us do the math.

Year Initial Interest Total
1 $1000 5% $1050
2 $1050 5% $1102.50
3 $1102.50 5% $1157.63
4 $1157.63 5% $1215.50
5 $1215.50 5% $1276.28

As you can see, there is a small decimal difference in the calculation. That is because we took 0.05 instead of 0.04999. That is not a big problem. You may remember that compound returns will give you accurate results in cumulative time periods. Not at the detailed level. Let us show you how. In the previous example, the beginning value was $1000 and the ending value was $1276.28. The investment became $1276.28 over a period of 5 years with 5% annual return every year. In reality, the annual return rate may fluctuate but after 5 years it will provide the same result. For example, look at the table below.

Year Initial Interest Total
1 $1000 0% $1000
2 $1050 -5% $950
3 $950 0% $950
4 $950 5% $997.50
5 $997.50 27.95% $1276.28

In this table, the annual interest rate was 0% for the 1st and 3rd year. It was negative 5% in the second year. In the fourth year it was 5% and in the final year the rate of return jumped to 27.95%, giving an equivalent value of $1276.30. Thus proving that compound return can provide accurate results in cumulative level but not in annual level.

Why do you need compound return?

You may ask, if compound return cannot provide accurate results at annual level, why do we use it? Is there any better method? Probably yes, there could be a method that can provide more accurate results. But compound return is easier to calculate and it has many useful applications for which investors and businesses use it regularly. First of all, compound return smoothens the annual return of an investment. Which makes it easier to compare that investment with its alternatives. Compound return can also be used for tracking and evaluating business performance. Investors also make use of this method to figure out how much they may get as return from the investment. For example, the investor has $20000 to invest today and he/ she needs a return worth $50000 after 10 years. They will simply take all the factors and put them in the formula of compound return to show an estimated result. If it’s over $50000, they will invest. There are more advanced uses of compound return in accounting, finance and business which cannot be done easily with other methods.

Final Verdict

Compound return may not provide accurate results at annual level, but it can show you the accurate result at a cumulative level. If you are ever confused on making an investment or cannot compare between the alternatives, remember compound return and use it. It will be a lot easier then.

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