Mortgage change of terms (lower rate) increases payment amounts

Question

My bank now offers lower interest rates than what I got when I first started my mortgage. I called to see about changing my terms (lower rate, same payoff date), and they said it would actually increase my payments slightly. My mortgage details are as follows:

Principle (p): $175,000
Acquired loan in: 2012
Term: 20-year, bi-weekly (26 payments per year = <20-year pay off schedule)
Payoff date: 2030 (14 years left)
Current interest rate (i): 3.4%
New interest rate (i'): 2.6%
The new loan would have the exact same payoff date, the same principle, and no points. The only added expense is a $950 fee upfront to change the interest rate.

I wasn't clear on their explanation of why my payments would go up, but it had something to do with restarting the interest payments. I understand that when you take out a loan, you pay mostly interest and little principal in the beginning and then mostly principal at the end due to the amortization schedule. My understanding, which I guess is wrong, was that the amortization schedule works by setting your payment such that your first payment is just a little higher than the amount of interest you accumulated that period, e.g. a $100 loan with a 1% monthly rate, you've got $1 in interest after the first month, so your first payment could be $1.20 with only $0.20 going towards the principal. Your $1.20 monthly payment will be almost all principal when the loan gets down to $5.
In my situation, this would mean that my next bi-weekly payment will be about $230 towards interest and the rest towards the principle.
p * i / 26 bi-weekly payments per year= $228.85

If my rate drops to 2.6%, I would pay $175 towards the interest and the rest towards the principle.
p * i' / 26 bi-weekly payments per year = $175.00$$

My new monthly payment would have to be such that the amount of principal I pay off each month would be small enough that I would still have the same payoff date, so I would expect my payments to go down. I must be missing something since the bank said the payments would go up slightly. Does what the bank said make sense?
Update
Turns out the bank made a mistake when they quoted me the payments the first time. After pursuing this further, as was suggested, the bank revised their payments to be ~$30 less than I pay now (current p+i = $613.12, new p+i = $585.98 at a rate of 2.55%). At 26 payments per year, I save ~$700 per year and about $9,000 over the life of the loan (after a $950 rate reduction fee).

Aganju · Accepted Answer

The interest part of the payment cannot go up when the interest rate is lower.

That said, your total payment might go up, because

the term was shortened, even slightly (you finish the complete mortgage earlier), so you pay more principal per payment
the refinanced amount is higher than the remaining amount ('Cash-out'; most people love that concept because the get an extra 2, 3, 5 or even 10 k$ cash in hand right now which they can use for that 600-inch-color TV they dream of and it's rolled into the mortgage); or significant closing cost are rolled into the total (and neglected to be pointed out to you...)
there are Points involved, and they didn't point that out. Points are minor adjustments to the interest rate that are prepaid/prereceived, for example, they are really offering a mortgage for the market price of 5.05 % APR, but to make it look better, they advertise it as 4.99 % APR, and the remainder is added up over the whole n years into one total and you pay that upfront as 'points' (or roll it into the total mortgage amount, so it becomes a bit higher)

The Points concept can become very confusing, and it works sometimes the other way round (you get a slightly higher nominal interest rate, and some cash in hand to make up for it)

Overall, the difference between 3.4 % and 2.6 % is large enough to seriously consider it, and I recommend you put the effort into really understand what is offered and how it is calculated. You can save significant money if it is real (or waste some if it's not real).

mhoran_psprep · Answer

Two notes must be addressed first:

A 20 year mortgage started in 2012 would be done in 2032 not the 2030 noted in the question. I am assuming that the remaining period as stated in the question (14 years ) is correct.
The payment each month is only Principal and interest. You are not looking at taxes and insurance. While they should not change because you are not changing banks, I can't rule out the fact that the new loan could be using a newer assessed value when determining the correct amount for property tax.

Using the exact values supplied in your question:

The old biweekly mortgage with exactly 14 years remaining would have a P&I of $604.54 a payment.
The new biweekly mortgage with exactly 14 years remaining would have a P&I of $573.50 a payment.

What isn't included is the closing costs. Though they are not as much as the original transaction because there is no real estate agents involved, but those costs do exist. One that is easy to overlook is points you are rolling into the mortgage. But there are also amounts collected by the state and local government; the appraisal company, Title Insurance...

For the numbers provided in your question if the closing costs exceed $9375 and they are rolled into the loan, then the new payment will be higher.

Mortgage change of terms (lower rate) increases payment amounts

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