I am currently reading an investopedia article about expense ratios in funds. This article uses the following numerical example about expense ratios and returns.
A fund has a gross return of 10% and an expense ratio of 1.5%. Therefore the net return of the fund becomes 10% - 1.5% = 8.5%.
I am trying to figure out what mathematical formula, relating gross return and and expense ratio is used to compute this net return. I know the following
Gross return = (Final investment - Initial investment)/Initial investment
And from the investopedia article, expense ratio is defined as
Total fund costs / Total fund assets. Which in this case I would assume is equivalent to
Total fund costs / Final investment.
So setting up the formula used to calculate the net return in the numerical example above, I get.
Net return = (Final investment - Initial investment)/Initial investment - Total fund costs/Final investment
I find this to be a strange result. Simplifying this equation doesn't get me a sensical answer.
So my question is how can you set up the formula which computes the 8.5% net return in the example above which includes the definition of gross return and expense ratio? I cannot seem to find a mathematical answer to this question.