REFINANCE A SECOND MORTGAGE - DIY AMORTIZATION AND PAY OFF AMOUNT

In the monthly loan payment article we presented a simple formula to calculate the amount of a monthly loan payment on any compound interest loan, which is almost every home mortgage loan and car loan. The only special equipment you need is a calculator with a power function key. That's the key with the y superscript x (y ^ x). If you have kids in school you probably already have one. If you want to practice with real numbers, you can get free actual 2nd mortgage refinance quotes here.

Here is a review of monthly payment formula that we used in our hypothetical second mortgage refinance problem.

The variables are:
N = mortgage loan period in months. i.e. 20 years = 240 months.
R = mortgage interest rate in whole numbers. i.e. 8% written as 8.
P = principal amount of the mortgage loan. The amount borrowed.
Q = the Q factor. An intermediate calculation.
M = home mortgage monthly payment amount

Here's the entire formula for the monthly payment amount of any compound interest loan:

M = (P * R * Q) / (1200 * (Q -1))

Easy enough, but first you have to calculate the intermediate value of Q. Here is the formula:

Q = (1 + R/1200) ^N.

Pretty simple, but you do need the power function key. N can get large.

In our earlier example we calculated a monthly payment of $418.22 on a $50,000 second mortgage at 8% for 20 years. You have paid the 2nd mortgage loan for 5 years (60 months). The pay off amount is $43,763 (rounded). This is how to calculate the amortization or pay off amount on any compound interest loan after N number of payments.

This is a three step process with a subtraction at the end. First calculate the growth value of the loan amount (P). P inflates by a factor of (1 + R/1200) per month, so after N months the value of the principal amount of the loan would have inflated to P * (1 + R/1200) ^ N. For the hypothetical $50,000 second mortgage with an 8% interest rate that has been paid for 5 years (60 months) the calculation looks like this:

50000 * (1 +8/1200) ^60 = 74492.28 (step one)

The monthly payments have also inflated by a factor of (1 + R/1200) per month so in math talk we have a geometric series with n terms. The monthly payment part of our hypothetical second mortgage is a little more complicated. The formula looks like this:

1200 * M * ((1 + R/1200) ^N -1) / R

Plug in the actual values and it looks like this:

1200 * 418.22 * (1 + 8/1200) ^60 / 8 = 30729.49 (step two)

Now finish up by subtracting the inflated payments value from the inflated loan amount value to get the amortized pay off amount for the current hypothetical second mortgage:

74492.28 - 30729.49 = 43762.79 (amortized pay off)

We have some good online refinance calculators here but we hope you write down the monthly payment and loan amortization formulas and stick them in your briefcase or your purse. For one thing, doing these loan calculations by hand will give you a greater sense of involvement and control over a very important aspect of your life. Another is that you aren't always near a computer when you think about refinancing your mortgage or your car, or the hundred other things you want to know about money and compound interest..

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