# Calculate T-Rex score step by step

I am having problem calculating T-REX Score which is given here https://larrybates.ca/t-rex-score/.

I can calculate my T-REX Score by putting my data in the calculator given in that website.

But I am curious on how to do it step by step?

Does someone know how to do mathematically?

If the amount invested is 1000 for a time of 5 years with an annual return of 8% and fees of 2% what is the T-Rex score?

• A little commentary about your source: Your goal in investment should never be to "beat the bank". If you have a personal hatred for banks and don't want them to make any money off of you, don't be their customer. Then they make nothing off of you. Your goal should be to find the investment strategy with the best ROI for you. How much or little money others makes in the process is pretty irrelevant for you. – Philipp Sep 26 at 10:19
• @Philipp; I get that,Thank you – Math_Freak Sep 26 at 11:41

Based on the calculator they are doing the following:

``````you_invest=10,000
annual_return=6.4%
years=25
total_gain = ((you_invest)*((1+annual_return)**years))-you_invest
total_gain = (10,000*(1.064**25))-10,000 = 37,156.40

annual_fees = 1.75%
effective_return = annual_return-annual_fees
effective_return = 6.4%-1.75% = 4.65%
gain_you_keep = ((you_invest)*((1+effective_return)**years))-you_invest
gain_you_keep  = ((10,000)*((1.0465)**25))-10,000 = 21,151.63

T-Rex score = gain_you_keep/total gain = 21,151.63/37,156.40 = 56.93%
``````

They are making a simple assumption that you subtract the percent fees from the gain. It does not factor in taxes.

The website even has an explanation about the math:

• Thank you so very much for your explanation – Math_Freak Sep 26 at 11:41

An investment with an annual return of 8% and an annual fee of 2% is an investment with an annual interest of 6%. You simply subtract the fee percentage from the return percentage.

And then you simply use the compound interest formula we all learned at school:

``````endCapital = startCapital * (1 + interest) ^ duration
``````

So with a start capital of 1000, an interest rate of 0.06 and a duration of 5 years you end up with \$1000 multiplied with 1.06 to the power of 5, or \$1338,23.

Now this does of course assume a very simplified situation: That all the fees are a yearly percentage of the capital you have at that time. Fees for financial services in the real world can also appear in lots of different forms:

• Up-front fees you need to pay at the beginning of the investment. They need to be subtracted from your start capital and thus your capital growth.
• Fees you have to pay to liquidate your investment, so they lower your end capital. Those might be either flat or percentual, but in either case they need to be subtracted from your end capital.
• Fixed annual fees. A fixed fee you pay every year which is independent from your capital at that point. Those make stuff really complicated because your ROI now becomes variable each year.
• Does someone know the formula for calculating compound interest with a fixed annual fee? My math skills are too weak for that, so my approach would be to just solve it algorithmically. – Philipp Sep 26 at 10:16