My total compensation is $168k/year ($285k gross) and my goal is to purchase a house in the range of $1M to $2M. I plan to invest my savings in the S&P500 for about 10-15 years, hopefully, to make ~$1M, and then use a mortgage to pay the rest of the house cost.
It is well known that the historical rate of return of the S&P500 is 10% (although I know that for all recent periods of 10 years, it has been either higher or lower than 10%). Doing the calculations (e.g., using this bankrate calculator), if I make an initial investment of $50k and then invest $5k/month with a hypothetical return of 10% and inflation of 2.5%, and a long-term tax rate of 15%, after 12 years I should be able to have ~$1M, thus being able to achieve my goal.
My question is that is there any wrong assumptions I have made or anything important that I have not included in my plan?