I started the process by first calculating various mortgage payments that I would feel comfortable with in order to find the range that fits my budget. That's the easy part.
I chose a $600,000 mortgage as the baseline because property here is really fucking expensive, and it's at the very top end of my price range. From there I decided I wanted to see what the ideal monthly payment would be assuming I had $100k to put down. I went into this with the assumption that paying off the mortgage as quickly as possible was the ideal because it would mean I pay less money to the bank in interest.
I took that down to $6900/mo which is outside of that screenshot, but not the point anyway. As you can see, the higher your monthly payment the less years you take to pay it down, and the less interest you end up paying. I thought to myself 'awesome', that's the way to go. Then I said 'wait, you're forgetting your project management course from college' and decided that the really important thing to look at was what I created on the last line of those iterations titled "Alt Invest %". That's the equivalent investment rate i.e. if you took that extra money you spend on a mortgage every month and invested it in a government bond paying ~2% you would make the same amount of money that you save on interest.
What's really interesting here is that on many websites, and in many conversations I've had, I've always been told that making an extra mortgage payment every year is ideal because it knocks 5-7 years off the mortgage. If you do that, you are actually near the bottom return possible, at 1.925% in this case. It's just about the worst thing you can do if the goal is to maximize your wealth generation over the long term. So much for that advice.
Ok, now what about down payments? Just like the extra monthly mortgage payment, everyone has always told me to put as much down as possible in order to decrease your monthly payments. That sounds like good advice, kind of (ignoring inflation), but of course I had to test it.
Given the same $600,000 price tag on the home and the $100,000 possible down payment, I decided to see what would maximize my return long term.
I decided to see what the difference was between putting $25,000 down and investing the remaining $75,000 elsewhere, 50/50, 75,25, and 100/0. This one is a bit different, because it depends entirely on what your alternative investment rate is. The screenshot above has an expected yearly return of 6%, the screenshot below has an expected return of 3%.
As you can see, if you have an expected yearly ROR higher than the interest rate on your mortgage, it is better to put as little money down as possible. If you are risk-averse and expect to see a lower annual ROR, you'd be better off maximizing your down payment.
In conclusion, you take a loss every time you put more money into your house rather than putting it in other investments (as long as the alternatives beat ~2%), and you maximize your long term investments if you minimize your down payment (assuming you can beat the interest rate paid to the bank). Personally, I will be putting the minimum down and pay the bare minimum payment on my mortgage. The emotional boost from paying down the house early just isn't worth it to me.