Imagine you want to copy a popular investor. First thing you may check is his or her performance. Your broker often only show us the performance in a specific year or time window. It doesn’t tell us the total performance and it also doesn’t tell us the average yearly return. How can we calculate it ourself?

Unfortunately, it is not enough to sum the yearly returns. That’s because of something called compounding effect.

## Compound interest

Compounding effect, aka compound interest, is like getting a reward not just on your initial amount but also on the interest you’ve already earned. So, it’s like your money is growing and making more money on itself. Let’s see how it works:

- You start with $100 in your portfolio.
- You earn 5% interest or profit, which gives you an extra $5. Now you have $105.
- The next year, you earn 5% interest on $105, which is $5.25. Now you have $110.25.

See what happened there? In the second year, you earned interest not just on your original $100 but also on the $5 interest you earned in the first year. This compounding effect makes your money grow faster over time.

## How to calculate compound interest growth

As explained above, a 5% profit or interest is going to bring your portfolio from $100 to $105. We are basically multiplying the original portfolio value by 1.05.

There are two components in the 1.05, 0.05 is equal the 5% profit, while 1 is equal to the 100% of portfolio you had at the beginning. Therefore, initial portfolio + profits.

If next year we make another 5%, we will reach $110.25, and if we want to do this for 5 years we perform the following calculation

initial portfolio * 1.05 * 1.05 * 1.05 * 1.05 * 1.05

This is equal to initial portfolio * 1.05^5 so we can use power to abbreviate the calculation. If the number of years is 10, then we change 1.05^5 with 1.05^10.

## How to calculate compound interest growth

Now let’s assume that instead of having the yearly profit we have the total profit and we want to calculate the average yearly return.

Let’s imagine that in 5 years our portfolio growth 200%. This means that our portfolio went from $100 to $300, with a $200 profits. Using the same notation as above that is $100 * (1 + 2) = $100 + $200. $100 is the initial portfolio value and (1 + 2) is the profit and loss. Let’s take the (1 + 2) = 3 and transform it to annual performance. Previously we were doing 1.05^5, now we have to do the opposite.

3^(1/5), where 3 is the P&L, and 5 is the number of years. If we perform the calculation this will give us ~1.25, meaning that our portfolio is multiplied by 1.25 every year, which is equivalent to 25% growth.

## Calculate PI returns in Excel

Let’s try to calculate this in MS Excel.

We start from a list of profits organized like this:

Now we need to add 1 to all of them and multiple them. Because the are all different profits we can’t use ^years anymore.

We can easily do this in Excel using this formula

Now we need to subtract 1 and change the cell format to %.

That is our total profit.

Let’s use this to calculate the average yearly profit. First we reintroduce the 1 that we subtracted. Then we use the formula explained above ^(1/number of years).

Next, we subtract 1, and we change the format to %.

The final results should look like this

## Conclusion

Compound interest means your money grows faster because it earns interest on both your original amount and the interest it has already earned. This is important to understand when you want to calculate how much your portfolio will be worth in the future.