The interest
schedule "starts over".
Which means when you refi to the same 30 yr schedule (and, yes, at a slightly lower amount, based on the amount you refinance), the fraction of your payment going to interest starts over. And in the first 1/3rd of your loan, most of your money goes to interest on the loan, not paying down the principal.
Ergo, if you borrowed 100k at 4.5%, then refi to another 30 yr at 3%:
- You already paid $40k in interest (~$60k total)
- You still owe about $80k
Refi to 3% and you "drop your payments" on the new $80k loan
Over the next 10 yrs you'll pay another $21k in interest and have only paid down another $20k in principal.
You still own $60k on your "new" 30 yr loan, and you've already paid that much in interest. Pay the rest of that out, and you end up paying $80k in total interest on the original 100k loan + new 80k loan.
Ends up being about the same total interest payment as the original 4.5% loan, only you took 40 yrs to pay it off, instead of 30.
If total interest is, worst case, the same, then that's not a big deal, and if you can refi and afford to pay off faster at the original payment, then you will end up paying less in interest.
Again, pay attention to your total loan interest, and what it may be if you can pay off faster at the lower interest rate.
Note that the refi to the "new" 80k loan at 3.5% (1% drop in interest) will end up costing you $10k more in interest (about 90k in interest between the two loans), than the original loan. And, again, that is IF you only pay on the schedule and not pay it down faster.