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# Help me with some simple math

Posted by Kromey at 8:51pm Sep 17 '12
So last week I made my first mortgage payment. Well, my first two, actually, owing to the fact that I have two mortgages, the sum total of which adds up to the purchase price of our house. (It's just how the no down payment, 100% financing deal worked -- two banks pick up and split the liability.)

Anyway, it got me thinking: I know that paying as little as \$20 extra per month can shave a full year and more than \$7,000 from my total payments. But, with two loans, is there a more advantageous strategy?

Consider the specifics:
Both mortgages are fixed-rate at 4.375%, for 30 years. Mortgage A has the bulk of the principal (\$200,600), while mortgage B has what really amounts to a token amount (\$35,400). Additionally, my property taxes and homeowner's insurance are rolled into the monthly payments I make to A; my payments to B then are strictly loan payments.

Now for the assumptions:
Assume I have a fixed amount each month to add to my monthly payments; let's say it's \$50.
Assume that if one mortgage is repaid, I will immediately shift the amount I was paying on that one to the other, i.e. the entire monthly payment (including all extra).
Assume that I will not refinance (for calculation purposes, that is).

My thoughts:
First off, I've been too long out of school to remember how to crunch these numbers, so these are just my hunches, although I like to think they're based on some primal knowledge of maths still in my brain somewhere.

However, I have two competing theories:
1) I should put the entire extra \$50 toward the larger balance, A, because 4.375% of that (yes, I know the APR and actual annual interest are not the same, but this is good enough since both balances have an identical rate) is much more than 4.375% of B, and therefore paying down the larger balance faster will have a greater impact on how much I pay overall.

2) I should put the entire extra \$50 toward the smaller balance B, because it will be affected a lot more and therefore paid off a lot faster, and then I can take that payment and direct it wholly at A to pay it off faster.

added on 9:11pm Sep 17 '12:
I forgot to add competing theory number 3:
3) It makes no difference, since both balances have the same interest rate attached, and X% of Y is always X% of Y. Therefore any advantage to pre-paying one over the other is purely psychological.