Paying Extra Towards My Mortgage

Can someone please explain how the duration of a mortgage goes down as extra money is being applied to the principle each month?

2 Answers

A loan has what is called an amoritzation schedule.  If it is due to be paid in 360 equal installments, the schedule denotes what portion of each payment goes to principal and what portion goes to interest.  Mortgage loan interest is calculated on a simple interest model which means you pay interest on the money for the period of time that it is borrowed. 

For example, a loan of $150,000 at 5.75% will have 360 payments of $875.29 [some differences may occur based on rounding].  The very first payment will have the most interest.  $718.75 out of the total will be applied to interest.  That is Principal  X Rate X Time = Interest for Period.  P = $150,000  R = 0.0575  T = 30/360ths of a year.  $150,000 X 0.0575 X 30 divided by 360 when you plug in the numbers.

The 2nd payment will be based on a new balance of $149,843.46.  Interest for month two will be $718.00.  The difference goes to principal.  And a new calcualtion is done for month 3, etc.  BUT, if an extra $100 is paid with the first payment, then $717.52, not $718.00 would be month 2's interest.  This may not seem like much, but it has a cumulative effect and it will mean that the loan will not need 360 payments to fully amortize [or be paid in full].

This only occurs if you have a fixed rate loan of course.  And it assumes all months are equal, hence the 30/360 formula.  Installment loans use actual days and a 365 or 366 day year.

It all boils down to simple Algebra. There is a payment formula that is used to calculate monthly payments on amortized loans with a fixed APR over a finite number of months.

Payment formula: Pmt = (((r(1+r)^n)/((1+r)^(n-1))) * L.

r is the periodic interest rate, n is the number of months financed, and L represents the loan amount.

If you have a loan in the amount of $200,000 with an APR of 6% (periodic interest rate is .06/12) financed for a 30 year period (360 months). You will have a monthly payment of $1190.10.

Your total payments will be $431,676.38 with finance charges totalling $231,676.38.

Now if you do a little Algebra, and substitute Pmt + x for Pmt, where x represents an additional payment, and solve the pmt formula for n you will get.

n = ln(((Pmt + x))/((Pmt + x)-(rL)))/ln(1+r).

let Pmt + x = $1,500 ( x=$500.90)

By doing the math your new n will be 220.20. Therefore you will pay off your loan in roughly 220 months.

Your total payments will be $330,406.96 with finance charges of $130,406.96.

You will save $101,269.42, and you will also pay off your loan in 220 months.

Note: The payment amount and other calculations are rounded. An additional amount will have to be paid on the 220nd month or 221st month since there is an additional 0.2 month after the 220nd pmt.