What is the mortgage equation?

Question

I am trying to see how which is best 15 years or 30 years. If it don't make a big difference.

I got appraisal at 15years for 5.875%
30years for 6.02%
My loan amount is $172,000.

HOw is it calculated or what is the equation?

I know some sight offer automatic calculation but I would really like to see the equation and how it is input?

Thanks very much.

Answer 1

The mortgage calculator at http://www.moneychimp.com/articles/finworks/fmmortgage.htm also provides the formula (scroll down) for making the calculations.

Answer 2

Gary was completely out to lunch. Gary's calculation would be correct for interest only, never reducing principal, but that wasn't what you asked. That isn't the way you calculated an amortization. In a true amortization, you pay a little of the principal every month (at first) which reduces the overall loan balance. By the second, third, fourth year, etc., the amount of the payment that goes towards interest decreases and you work on paying the loan down. By then end, it is mostly (or all) principal.

15 years at 5.875% for $172,000 is paid back at $1439.84 per month. Total interest paid over the life of the loan is $87,171.89

30 years at 6.02% for $172,000 is paid back at $1033.44 per month. Total interest paid over the life of the loan is $200,033.

As you can see, you will pay more per month with the 15 year loan and save yourself in excess of $113,000 over the life of the loan.

a = [P(1 + r)^n r]/[(1 + r)^n - 1]

a is the payment. P is the principal and r is the rate and n is the term. If you are trying to do monthly, the interest rate has to be converted into a monthly rate.

Find a good amortization calculator on the web. They are a dime a dozen.

Answer 3

Principal x Rate x Time = Interest
Principal + Interest = Maturity Value

For 15 years:
$172,000 x .05875 x 15 = $151,575 (Interest)
$172,000 + $151,575 = $323,575 divided by 180 pymts =
$1,798 approx monthly payment

For 30 years
$172,000 x .0602 x 30 = $310,632 (Interest)
$172,000 + $310,632 = $482,632 divided by 360 pymts =
$1,341 approx monthly payment

These monthly payments do not include property taxes and homeowner's insurance.

Answer 4

m=12 assumed monthly compounded
yr=15 years amortized
n=m*yr
=12*15
=180
%int=5.875 annual interest rate
int=%int/100/m
=5.875/100/12
=0.004896
F1=interest portion of equal monthly payment
=PV*[(1+int)^(m/12)-1]
=172000*[(1+0.004896)^(12/12)-1]
=842.08
F2=monthly equal payment factor
=[1-(1+int)^(-n)]
=[1-(1+0.004896)^(-150)]
=0.5848
PMT=monthly equal payment = interest + principal
PMT=F1/F2
=842.08/0.5848
=1439.84 ans #1

similarly for yr=30 and %int=6.02 my computer excel program said
F1=862.87
F2=0.8349
PMT=1033.44 ans #2

i would compare the amount of interest paid.
F1=842.08 for 5.875%15yr (this one is better)
F1=862.87 for 6.02%30yr

compared based on interest payment is suggested because the interest is a gift to the bank. but you could choose to compare based on monthly payment (PMT) if the money is tight.