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Summary: When you refinance your house and borrow more money, how to calculate the incremental interest rate you pay?

I currently owe $95K on my house, 4.75% interest rate, $510 monthly payment (principal and interest, excludes escrow), 28.75 years remaining on 30-year fixed rate mortgage.

I'm looking to refinance for $128K, 5.625% interest rate, $737 monthly payment, 30-year fixed mortgage.

I think 5.625% is a good rate to borrow money, but that's not exactly what's happening here.

Instead, I'm getting an extra $33K, but paying a higher interest rate on the entire $128K.

What interest rate am I effectively paying on the extra $33K that I'm borrowing?

For example, I'm effectively paying $227 per month to borrow $33K. What rate does that work out to?

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A payment of $224 at 7.2% interest will pay off a $33000 mortgage in 30 years.

Unfortunately, I'm on cold medicine so guessing was the only way I got to the answer, but I guessed right on the first try :).

However, if you like algebra:

The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

P = L[c(1 + c)n]/[(1 + c)n - 1]

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$33K, $227 payment is 7.33%. But is that right? You're also stretching out the remaining loan back to 30 years. Now, if the bank just let you do the stretch, you'd owe

$95K / 4.75% / 360 mo / PMT = $495.56 - this would be a neutral move, same rate.

You now have: $128K / 5.625% / 360 / PMT = $737 so to my thinking, the delta is:

$33K / X rate / 360 / PMT = $241.44 and the rate is 7.97%

If you have enough equity to refi, you have enough to take that in a HELOC, and pay it off aggressively, why give up the great rate? The $227/mo you will pay the HELOC off in 22 years even at 6%. My HELOC is 2.5%. I'd use any raise or bonus to hack away at it.

I tried to spell out my thought process on the math. If any savvy reader (you all are, I know) wants to look at this and offer a better method, I'm open minded. There's a fallacy that comes with refinancing, certainly money appears in the payment stream as a result of extending the term. Somewhere that needs to be accounted for, else a higher rate at a longer term appears favorable, so my approach is to normalize the numbers one way or another. Here, producing that first step of calculating the payment on the extended term (an interim step that's a mental process only, that loan is hypothetical). Comments welcome.

  • I didn't realize stretching the loan from 28.75 years to 30 years would lower the mortgage that much (I realize $14/month isn't a "lot", but, as you note, it's not ignorable). Between that and closing costs, I'm starting to wonder. Are there HELOCs with a fixed interest rate or capped rate increases? All the ones I've seen are variable rate change-any-time-by-any-amount types. I suspect interest rates will get much higher in the next few years, so I try to avoid variable rate loans (although variable rate + cap might be OK). – barrycarter Dec 25 '10 at 16:20
  • There are many deals out there, you may find a fixed 20yr equity loan at a decent rate. I suggest you shop around. In my math, we didn't even take closing into account. So instead of $241 being the payment on $33K, maybe it's only on $30K, sending the rate higher. Keeping looking my friend, I hate to see you give up that 4.75%. – JoeTaxpayer Dec 25 '10 at 16:25
  • Is getting a 2nd mortgage an option? If I understand correctly, that means keeping my existing loan, and getting a new loan on the additional equity? I'm guessing rates aren't very good for that because no one wants to be the second default creditor on a house? – barrycarter Dec 26 '10 at 19:59
  • Yes, it's an option, just like a HELOC is an option. You should look in the local paper and see what banks are offering. Worse case, you can't do it an go to plan A. Best, you find a decent rate and keep your first mortgage. For the money involved, it's just worth a bit of research. – JoeTaxpayer Dec 26 '10 at 23:20

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