Small Surplus in Budget... Pay Down Principal or Put in Savings?

[Jason Thornberry]

Lets say you have a standard 30yr Fixed Mortgage with a rate of 3% and a balance of $100,000.

Now lets say you have an extra $100/month that you could use to pay down the principal OR you could put it in a saving account and earn 4.5% APY.

On the surface, earning 4.5% sounds like the smarter choice.  However, after giving it a little thought, you realize that after a year, 3% of 100k is $3000.  Whereas, 4.5% of 1200 is only $54.  (This is over-simplified but I hope you can see where I'm going)

I'm not sure how to do the math to see the exact figures in both cases to determine amount saved vs amount gained over time.

There's got to be a formula or a calculator somewhere but I'm not having any luck with search results using my existing (limited) terminology.  Can anyone point me in the right direction?

[Bill B.]

Your $100 is going to save $3/yr or earn $4.50/yr. If you had a $1million loan you’d be paying $30k/yr in interest, it has no bearing on your $100. What’s more 4.5% will double about once every 16 years while 3% would take 24 years. So in 48 years you can have 4x your money or 8x your money. 

If you don't itemize you would pay tax on the savings account while paying off your mortgage wouldn’t cost you any tax savings, a tiny variation that makes paying off the mortgage “less bad”. BUT, $1,200 in the savings account is cash you have access to when the ac unit dies or you have a medical emergency. Owing $1,200 less on your mortgage provides zero extra security.