How to calculate incremental interest rate for home refinancing?
Summary: When you refinance your house and borrow more money, how to
calculate the incremental interest rate you pay?
I currently owe K on my house, 4.75% interest rate, 0 monthly
payment (principal and interest, excludes escrow), 28.75 years
remaining on 30-year fixed rate mortgage.
I'm looking to refinance for 8K, 5.625% interest rate, 7 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 K, but paying a higher interest rate
on the entire 8K.
What interest rate am I effectively paying on the extra K that I'm
borrowing?
For example, I'm effectively paying 7 per month to borrow K. What rate does that work out to?
(2)2 Comments
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K, 7 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
K / 4.75% / 360 mo / PMT = 5.56 - this would be a neutral move, same rate.
You now have:
8K / 5.625% / 360 / PMT = 7 so to my thinking, the delta is:
K / X rate / 360 / PMT = 1.44 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 7/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.
A payment of 4 at 7.2% interest will pay off a 000 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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