I'm looking to do a pretty basic Finance 101-type calculation to compare final portfolio values given varying fees.
Let's say I start with a $50,000 portfolio. It's invested in a fund that returns 7%/year with an investment horizon of 15 years.
Scenario 1: Low-cost, passively managed fund with an annual expense ratio of 0.05%
Scenario 2: Actively managed mutual fund with an annual expense ratio of 1.00% (assuming it also returns 7%)
I'm trying to figure out:
(A) how much the $50,000 is worth at the end of 15 years, given the 7% growth rate
(B) what the difference is in value if I go with Scenario 1 vs. Scenario 2, eg, how much money I leave on the table just by paying that 1% for active management
It's easy to plug this into an online calculator or model the annual returns in XLS, but I know there's a more parsimonious mathematical way to do this calculation (something with geometric sums, I seem to remember?)