You're forgetting your regular mortgage payments in the "put the extra into savings" scenario.
You've already got 46K in equity in the house either way, so in the "savings" part of the formula, you've got 63K in cash + 46K in current equity + equity gained from appreciation (you may not be considering this on the "extra to mortgage option", in which case it should be ignored here too) + equity gained from regular payments, which over 5 years is pretty significant.
Putting the cash in the 1% savings account means you'll likely have a little less total "housing money" than putting it all into the house, but it isn't close to 140K vs. 63K.
Having some cash around for the purchase can be good. Earnest money and inspections have to be paid for. You can make a cash down payment if your house hasn't sold, but you need to move on the new place. Your old house may have gone down in value in the interim and eaten up a chunk of that equity you were counting on.
Here is the line item from exactly five years from now simply paying my current payment...
Date Payment Payment2 Interest Principal Total Interest Extra Payment Balance Equity
6/1/20 92 $759.75 $267.47 $587.22 $30,109.66 94.95 $81,597.62 $83,402.38
Here is the line item from exactly five years from today adding in an extra $500 per month (on top of what I'm already paying)
Date Payment Payment2 Interest Principal Total Interest Extra Payment Balance Equity
6/1/20 92 $759.75 $267.47 $1,087.22 $30,109.66 594.95 $51,097.62 $113,902.38
That gives me $113,902 (even though the money is tied up in the house) to use towards a down payment.
With option 1 I will have theoritcally taken that $500 and put it in a savings account earning 1% interest and on 6/1/2020 I will have $32,327.
Adding that to the equity I will have a total of $115,729. So in this scenario it actually saves me MORE money to keep paying the normal amount, plus I will have the piece of mind that those funds are liquid.
