Expense Ratio Calculator
The expense ratio calculator is a fantastic tool that helps you to understand how much you will pay for the performance of your exchangetraded funds (ETF) investments. In other words, it simplifies even the most effortless security, the ETFs. In this article, we will cover what an ETF is and how the expense ratio is related to it. We will also discuss what is a good ETF expense ratio and conclude by comparing it to famous ones: the SPY ETF and the ARKK ETF.
What is an ETF?
An ETF is a type of security that allows you to invest in a group of different companies at once. It is similar to a basket of several stocks. Components of an ETF are also known as holdings and are always diversified, meaning that you will find several different companies in the basket.
The main advantage of an ETF is that it allows you to quickly diversify your investment without needing a lot of money. For example, let's start with probably the most famous ETF: SPDR® S&P 500® ETF Trust (NYSEARCA: SPY). It contains approximately 500 companies which are known as the most representative of the USA stock market. Three of its components are:
 Apple (SPY portfolio weight 6.40%);
 Microsoft (SPY portfolio weight 5.40%); and
 Amazon (SPY portfolio weight 4.47%).
Those three represent 16.27% of the total ETF, or in other words, there is 83.73% of the SPY portfolio weight distributed in other companies. The current cost of this ETF is 357 USD (November 23th, 2020), meaning that your 357 USD investment will be distributed in the 500 companies accordingly to their portfolio weight, without requiring you to buy each of these stocks.
However, ETFs are not free. Please keep reading to find out what are their costs and how it impacts your investment performance.
What is the expense ratio?
The expense ratio is a fee charged by mutual funds and ETF providers for the concept of managing the assets in the fund. We can call it the maintenance fee of the investment. It usually ranges between 0.1 to 1%, but it can go as low as 0.045%, like in the SPY case, and up to 2.95%, like in the case of Global X SuperDividend® Alternatives ETF (NASDAQ: ALTY).
But, how it affects the return of your investment? Well, all ETFs and mutual funds have a yearly historical performance expressed in a percentage (in our expense ratio calculator it's called: Yearly expected investment return
). That is probably the most advertised value because it shows how much money the ETF and fund are expecting to be making in the next years.
However, that's not the money you receive. The actual performance of your investment is the ETF/fund performance minus the Expense ratio
you will have to pay every year.
Here it is important you remember the effect of the time value of the money formula and the compound interest formula. Both concepts explain how important those fees are. You might think that 0.1% is nothing, but if it compounds over time, it might be a relevant chunk of your money.
What is a good expense ratio?
According to Morningstar, the average ETF price is 0.45%. So, at first sight, any ETF expense ratio above that value has to justify its costs with an outstanding performance.
There are three main points we have to take into consideration when choosing an ETF as a long term investment:

We should always look for an ETF with a historical return higher than the general market's return. We can take the 10 years return of the SPY as a benchmark: 13.59%.

When we already have found a great
Yearly expected investment return
, we should look at the primary holdings and analyze its risk. 
Whenever it is possible to predict inflation through the duration of the investment, we should consider it as a yearly interest rate we should beat. If you are interested in to a calculator that includes effects of inflation, see investment calculator.
So, how to calculate the effect of the expense ratio?
If you already understand how to calculate the future value of money and future value of an annuity this will be easy as pay.
The calculation has two parts. The first considers an initial investment for which we will use the formula for the money's future value. The second one considers a yearly periodic investment for which we will use the formula for the future value of an annuity.
We will start defining the variables:

I_{0}
= Initial investment, or our first deposit; 
PI
= Yearly periodic investment or the money we invest every year; 
n
= Duration of investment, or the amount of time we will leave our money to grow; 
r_{effective}
= Effective investment return which will represent the real compounding rate our investments will have, discounting fees; 
r_{expected}
= Expected investment return, based in the historical performance of the ETF; and 
Er
= Expense ratio.
Then, the formula for Initial investment future value (FVI)
:
FVI = I_{0} * (1 + r_{effective})^{n}
where:
r_{effective} = r_{expected}  Er
,
and for the Periodic investment future value (FVPI)
:
FVPI = PI * ((1 + r_{effective})^{n}  1) / r_{effective}
Finally, for the future value of the total investment (FVTI), we will have:
FVTI = FVI + FVPI
If this was too much, don't worry, we integrate all of them into our expense ratio calculator, so you can play with the numbers as you wish until you get it.
How much does the expense ratio cost you?
For this calculation, we need to use the formulas mentioned above twice. First, considering a certain expense ratio and then without it. Consequently, we will have two future values for the total investment, which, after being subtracted, will result in the total cost.
ETF_{cost} = FVTI_{without_expense_ratio}  FVTI_{with_expense_ratio}
Of course, our beloved expense ratio calculator includes this functionality already.
Real example: SPY ETF vs. ARKK ETF
For this comparison, we will analyze two of the most famous and trendy ETFs of this year 2020: ARKK ETF vs. SPY ETF.
ARKK is an ETF that covers probably the most innovative and disruptive companies. Let's take a brief look: Tesla (NASDAQ: TSLA) is an electrical vehicle automaker that already provides selfdriving vehicles. This company, by the 20th of November, represents 9.71% of the total ETF. Moreover, SLACK (NYSE: WORK) is a company that provides a digital communication platform for work. It currently represents 3.27% of the ETF.
So, suppose we follow the next investing scheme:
Initial investment = 10,000 USD
Yearly periodic investment = 5,000 USD
Also, imagine we started at the inception of the ETF that was six years ago. Then, by considering the historical return since its beginning, which can you can find on the ARKK's webpage, we get:
Duration of investment = 6 years
Yearly expected investment return = 30.97%
Expense Ratio ARKK = 0.75%
Thus, by using our friendly expense ratio calculator, we get the following results:
Future value of total investment = 112,890.45 USD
Total cost of ETF = 2,916.27 USD
If you enable the advanced mode of the expense ratio calculator, you can get extra information such as the effective investment return you had, how much the initial investment and periodic investment grew.
Effective investment return = 30.22%
Initial investment final value = 48,760.27 USD
Periodic investment final value = 64,130.17 USD
Now, we are going to do the same calculation but with the SPY ETF information:
Yearly expected investment return = 13.59 %
Expense Ratio SPY = 0.0945%
and by using our Expense Ratio Calculator, we get:
Future value of total investment = 63,510.74 USD
Total cost of ETF = 207.66 USD
Similar to the case before, the extra information of the advanced section is:
Effective investment return = 13.49%
Initial investment final value = 21,373.31 USD
Periodic investment final value = 42,137.43 USD
As a conclusion, we can say the following:

It is clear to see that the compound interest effect over time of the
Effective investment return
can do a significant effect on your money. 
Moreover, the expense ratio calculator shows us the cost of each expense ratio, a difference of
2,916.27  207.66 = 2,708.61 USD
, which could definitely have hurt us if the ARKK ETF would not have had such a fantastic return. Consequently, we should only accept a high expense ratio if theYearly expected investment return
will cover the costs.
Finally, do not forget that high returns usually are connected with high risk meaning that the ETF may have lowreturn years. So it is strongly recommended to check how diversified the security is, especially the leading positions. You can conduct a quick but pretty complete analysis of them using our set of financial calculators.