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It is my understanding that biweekly payments that are applied to your loan reduce your principal 2 weeks before your monthly payment could lead to a shorter duration for the money owed. Please correct me if I am wrong.

  • Now, if the servicer doesn't allow partial payments and holds on to the partial (half) payment until the full amount is received, would it be possible to get the same amount of savings as a biweekly payment through other means? What's the math behind the alternative(s)?
    • I can think of paying an extra amount at the beginning of the year but is paying an extra payment amount at the beginning of the year better or the same than biweekly payments?

    • I have heard that paying 1/12th extra in each payment would be the same but I don't see how the math would help (because you owe a bigger amount each time a payment is due) unless I misunderstood the biweekly payments approach.

    • Is there a reason why servicers aren't forced to do this by law? I see biweekly payments as a way to help the consumer.

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    Didn't you ask this a few months ago? money.stackexchange.com/q/148393/5760 Jul 30 at 13:08
  • I am asking for the math and alternative to paying 1/12th. There's the part where I ask about paying 1 full amount at the beginning of the year. Jul 30 at 13:11
  • The only way to reduce the duration of the loan is to make more than the minimum payments, but it doesn't matter when you make those payments. If you made half-payments every two weeks (assuming your servicer allowed that), the duration of the loan would remain the same, but the total interest paid over that duration would be less, as the principal on which interest accrues would be smaller for the second half of the month.
    – chepner
    Jul 30 at 15:32
  • There is no reason to think that any practice on the part of the servicer should be illegal just because an alternative more favorable to the consumer exists. Servicers are entitled to protection under the law as well, so your argument quickly devolves into an argument against the legality of charging in interest at all.
    – chepner
    Jul 30 at 15:41
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    I agree with @DilipSarwate. The mathematical alternative that yields a very similar result is what you propose in the other question. 1 extra payment at the beginning of the year is slightly better than 12 extra payments of 1/12 each month, is (probably) slightly better than making 26 half payments. The difference between those 3 is small, compared to the fact that all of those are far better than making the minimum monthly payments.
    – TTT
    Jul 30 at 16:30

2 Answers 2

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I got the impression that you attribute the shorter runtime of the mortgage to savings on interest in those 2 weeks (e.g. you pay earlier, so you pay less interest). While it has an effect, the effect is actually small.

The big effect actually comes from paying more per year. If you pay half the monthly rate every two weeks, you pay 13 monthly rates per year (as the year has 52-53 weeks). Obviously, if you pay more rates per year, you pay off your loan faster.

And that is also where your 1/12 extra payment comes from: if you increase your monthly payments, you now pay 13 of the previous monthly rates per year, so the same total amount as in your bi-weekly payment.

It's still not exactly the same (the exact value would depend on the exact dates). But the difference can only be in the range of the compounded interest on a bi-weekly rate: just imagine if instead of a bi-weekly mortgage over $100,000 and $500 bi-weekly rates, you take out a loan of $99,500 and ($1,000+1/12) monthly rates. The total interest for the monthly payment must be lower (as the average outstanding amount is lower), so the difference between a monthly $100,000 loan and a bi-weekly $100,000 loan cannot be more than the total compounded interest on a $500 loan over the runtime of the mortgage. You can adjust the monthly payments to make up for that difference.

With the same logic: if you pay the missing amount (e.g. the 13th missing rate) at the beginning of the year, the outstanding amount for the monthly payments will always be lower than the outstanding amount for bi-weekly payments (and will catch up at the end of the year). If you do the payment in the middle of the year, it will almost average out (e.g. for the first 6 month, you pay more, for the next 6 month, you pay less).

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Assuming no prepayment penalty and simple interest, paying earlier will always reduce your payment duration. e.g., paying $1200 at the beginning of the year will reduce the duration by more than paying $100 a month. But the difference may not be large, for my example below, the reduction in duration is only two months. 301 payments vs 303 payments, but both are less than your original unmodified loan of 360 payments.

why servicers aren't forced to do this [biweekly] by law?

Not all laws are created to benefit the consumer. Banks lobby the government for laws that make more profit for them (which includes making life easier for them).

Since you are interested in multiple "what ifs", you should learn to calculate this yourself. Here is the Excel spreadsheet that I used. I believe that the results were slightly different than the bank calculations, but close enough for what you want to do. I've never used it for bi-weekly, so no promises on bi-weekly. Once the equations are entered, you should only change the top section and the "additional principle" column.

enter image description here

Here are the equations. Starting at row 16, they are the same, just "copy down".

enter image description here

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