How to determine new, lower interest payments after a lump sum mortgage payment, i.e. new amortization schedule?

Question

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.

Answer 1

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.

Answer 2

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.)

Answer 3

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)