For those following along and think better with actual numbers than theory, I worked something out so that I could better understand what's going on.

Assume you have $16k cash, $0 income, a house that will sell in a year for $200k after fees, and $100k mortgage 4% loan with $500 monthly payments.

If you just make the monthly $500 payments..

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```
cash: $15,500, interest paid: $333.33, principal paid: $166.67, loan balance $99,833.33
cash: $15,000, interest paid: $332.78, principal paid: $167.22, loan balance $99,666.11
cash: $14,500, interest paid: $332.22, principal paid: $167.78, loan balance $99,498.33
cash: $14,000, interest paid: $331.66, principal paid: $168.34, loan balance $99,329.99
cash: $13,500, interest paid: $331.10, principal paid: $168.90, loan balance $99,161.09
cash: $13,000, interest paid: $330.54, principal paid: $169.46, loan balance $98,991.63
cash: $12,500, interest paid: $329.97, principal paid: $170.03, loan balance $98,821.60
cash: $12,000, interest paid: $329.41, principal paid: $170.59, loan balance $98,651.01
cash: $11,500, interest paid: $328.84, principal paid: $171.16, loan balance $98,479.84
cash: $11,000, interest paid: $328.27, principal paid: $171.73, loan balance $98,308.11
cash: $10,500, interest paid: $327.69, principal paid: $172.31, loan balance $98,135.80
cash: $10,000, interest paid: $327.12, principal paid: $172.88, loan balance $97,962.92
```

Then after selling the house for $200k, you have $112,037.08 cash on hand.

If you pay down an extra $10k principal and still make the normal monthly $500 payments..

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```
cash: $5,500, interest paid: $333.33, principal paid: $10,166.67, loan balance: $89,833.33
cash: $5,000, interest paid: $299.44, principal paid: $200.56, loan balance: $89,632.78
cash: $4,500, interest paid: $298.78, principal paid: $201.22, loan balance: $89,431.55
cash: $4,000, interest paid: $298.11, principal paid: $201.89, loan balance: $89,229.66
cash: $3,500, interest paid: $297.43, principal paid: $202.57, loan balance: $89,027.09
cash: $3,000, interest paid: $296.76, principal paid: $203.24, loan balance: $88,823.85
cash: $2,500, interest paid: $296.08, principal paid: $203.92, loan balance: $88,619.93
cash: $2,000, interest paid: $295.40, principal paid: $204.60, loan balance: $88,415.33
cash: $1,500, interest paid: $294.72, principal paid: $205.28, loan balance: $88,210.05
cash: $1,000, interest paid: $294.03, principal paid: $205.97, loan balance: $88,004.08
cash: $500, interest paid: $293.35, principal paid: $206.65, loan balance: $87,797.43
cash: $0, interest paid: $292.66, principal paid: $207.34, loan balance: $87,590.08
```

Then after selling the house, you have $112,409.92. This is $372.84 more than the previous situation.

If instead you invested that $10k at 4% yearly interest compounded monthly..

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```
balance: $10,000.00 growth: $33.33
balance: $10,033.33 growth: $33.44
balance: $10,066.78 growth: $33.56
balance: $10,100.33 growth: $33.67
balance: $10,134.00 growth: $33.78
balance: $10,167.78 growth: $33.89
balance: $10,201.67 growth: $34.01
balance: $10,235.68 growth: $34.12
balance: $10,269.80 growth: $34.23
balance: $10,304.03 growth: $34.35
balance: $10,338.38 growth: $34.46
balance: $10,372.84
```

You also gain $372.84 at the end of that year.

If instead of $0 income, we're at 25% tax bracket, the first situation would have $3,962.92 interest to deduct while the second has $3,590.08 reducing the tax owed by $990.73 and $897.52 respectfully -- a difference of $93.21. And the $10k investment's gain of $372.84 taxed at 25% is $93.21 in extra taxes.