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Here's a financial math problem:

I have a mortgage at about $78,0000 with 5.5% interest and 56 of 360 monthly payments were made. I'm currently paying about $360/month in interest charges. If I pay it down by $50,000 what would the monthly interest payments be?

I've trying to build a amortization schedule, but the lump sum is difficult to represent. Do I just start over with 360-56=304 payments? It sounds like the bank will actually decrease the term of the mortgage. How is that calculation done? My main goal is to reduce interest charges. My second goal is to have a lower monthly payment.

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3 Answers 3

In a nutshell, yes, just generate a new mortgage schedule assuming the new principal amount and new number of payments. Spreadsheet software like Microsoft Excel have all of the formulas you'd need to build your own schedule, but let me show you a neat way to get the answer you want online:

Did you know Wolfram Alpha, the "computational knowledge engine", does mortgage calculations?

First, let's simplify two things before we plug into Wolfram Alpha:

  • New mortgage principal amount: $78,000 - $50,000 = $28,000 principal
  • New number of payments: 304 / 12 ~= 25.3333 years

If you input the following query at Wolfram Alpha (or just click my link here), you should get an answer: Wolfram Alpha: mortgage payments for $28000 USD at 5.5% over 25.3333 years

Here's a snapshot of some of the results. I've highlighted one number in particular: the first year's total interest paid, $1527. Divide that by 12 to get the average monthly interest paid in that first year: $127.25 per month. I hope that helps!

Note: The example doesn't factor in any pre-payment penalties (if any – check with your lender.)

Snapshot showing monthly payments, effective interest rate, mortgage totals, and amortization payment table for sample Wolfram Alpha mortgage query

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what the wolfram!?! That is a great use for that weird "knowledge engine" – MrChrister Apr 8 '10 at 16:45
Wow, very interesting. However, my lender said that the term of the mortgage would be reduced when paying it off in a lump sum. How does that work? – Benjamin Apr 8 '10 at 16:57
Yes, without re-amortizing the mortgage based on the new lower principal amount, any prepayments will otherwise just make your existing mortgage's term shorter. If you want to lower your monthly payments as stipulated at the end of your question, then you will need to ask your lender to re-amortize your mortgage, as this example has shown. There may be a penalty or fee involved; negotiate if necessary. – Chris W. Rea Apr 8 '10 at 17:23
Ah, I'm not sure how to say this. I want to lower my "interest payment" not my monthly payment and not my interest rate (5.5%). I want to be sure that when I pay the lump sum, the bank isn't charging me interest on the principal that I already paid off. – Benjamin Apr 8 '10 at 23:39
Then you want the shorter term in that case. Payments are the same $ per month, but there's a higher portion going towards principal, and less towards interest, because the bank only charges you interest on the principal outstanding. – Chris W. Rea Apr 9 '10 at 0:33

Ok, I think that I solved the issue. I made an amortization table in Excel. So far, everything seemed to match my bank statement. Then, I looked at the remaining principal for payment number 56 (78070.77). I scanned the rest of the table to find where the principal is $50k less (28070.77). I found payment number 291 had $28130.57. The new interest payment is $130.57 which is over $200 down from $358.30 and the term of the mortgage is shortened by several payments. It also looks very close to the result from Wolfgram Alpha. Maybe recasting is a better option since your monthly payment goes down and you can extend out the loan if you need extra cash.

Feel free to try it yourself. Here are my numbers:

Starting Principal: $83,920
Rate: 5.5%
Monthly payments: 360 (30 years)
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This sounds genius... I think that makes a lot of sense. I hope you're right about how this works. – ArtOfWarfare Sep 25 at 12:31

You do not get a lower required payment. You certainly save interest. And your mortgage will end far sooner. But, the standard mortgage, while permitting prepayments, structure it as an early reduction of principal, but do not calculate a new lower payment. The same amount is due until you've paid all principal to zero.

In response to the request in the comment below, I have a spreadsheet for downloading.

Note - it was written in response to a mortgage scam, but serves the purpose of evaluating time remaining on 15 or 30 year loans when prepayments are made. The sheet's equations are locked, you can only change your numbers. When I first offered it (free then, free now) too many people tinkered, broke it and asked for help to keep changing it.

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+1 I can't believe that this point was never brought up when this question was asked and answered three years ago. – Dilip Sarwate Sep 1 '13 at 12:26
Hi Joe, how do we determine how many fewer payments we have to make and how much less interest we'll need to pay? I'm not concerned about the size of future payments - I'm much more concerned about how many future payments there will be. – ArtOfWarfare Sep 25 at 12:32
@ArtOfWarfare - i added a link above for you. Please respond that you got it. Contact me through my site if specific questions, here if general. – JoeTaxpayer Sep 25 at 12:56
Thanks Joe - I'll play around with this later tonight. One thing I would just add to the top of the spreadsheet is just an indicator of when your balance will hit zero - right now you have to scroll through the list to find that. Not a biggie - something I can easily add myself. – ArtOfWarfare Sep 25 at 14:44
@ArtOfWarfare - Col H is "months remaining" No need to scroll, just divide by 12 to get "years". – JoeTaxpayer Sep 25 at 15:20

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