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I am asking about the mathematical formula, or constructing the amortized loan table, of the effect of someone prepaying their loan. According to this website, you'd calculate the monthly payment using the formula.

Now, let's say someone is prepaying their loan, not on a regular basis, but random amounts sprinkled throughout the lifetime of the loan. How do you recalculate the table? Obviously, the monthly payment amount is no longer the same. Do you take the current loan balance, reenter it to the formula, with reduced number of payments?

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For an amortized loan, you can calculate the monthly payment for a loan.

For example, 30 year loan at 7% for $100,000 would have a monthly payment of $665.30.

For the duration of your loan, your payment will be $655.30 no matter how much you prepay.

For each payment, you calculate interest owed (7% / 12 * Loan Balance). For the first month, you get 0.07/12*100,000 = 583.33.

For your first payment of $665.30, you'll pay $583.33 and $81.97 to principal.

This will reduce the mortgage balance to 99,918.03 for the next month. Month 2's interest payment will be 0.07/12*99,918.03 or $582.86 interest and $82.45 principal.

If instead, you paid $10,000 extra, your loan balance would be 89,918.03 and your interest would be 0.07/12*89,918.03 or $524.52 interest and $140.78 principal.

To determine how many payments are left, you calculate out how the principal reduces when keeping the payment constant and see when the loan is paid off.

Here's a reasonable calculator that lets you put in several one time payments or consistent repeatable payments: http://mortgage-x.com/calculators/extra_payments.asp

As an aside, the cost to pay a "month" of principal extra at the beginning of a mortgage is very small. At the beginning of the loan above you are paying $81.97 per month in principal. If you send an extra $82 to your mortgage in the first month, you reduce your mortgage duration by 1 month. $82 in month 1 means you save $665.30 during month 360. $165 in month 1 will save you $1330.60 during months 359 & 360.

  • Got it. The monthly payment remains constant, and interest is calculated when payment is due, and you just subtract from there. So the last payment would be in a slightly different amount then, depending on how much balance you still have. – garbagecollector Sep 29 '14 at 22:00

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