How to Calculate: Mortgage Payment Formula
Calculate, with the mortgage payment formula, your own mortgage payment price. For some people a simple amortization table in excel or a mortgage payment calculator just isn't enough. If that's you, read on. If not, check out related articles on the right sidebar below on how to use a mortgage payment calculator you can create using amortization tables.
Fully follow these steps to understand how compounding interest works in a mortgage.
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Instructions
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UNDERSTAND THE BASIC MORTGAGE FORMULA.
For the most part every mortgage is calculated based on this traditional formula. It takes into account the fact that mortgages (refinancing mortgages or first home loan mortgages alike) use compounding interest instead of simple interest. Here it is:
M = P [ i(1 + i)n ] / [ (1 + i)n - 1]
M = mortgage payment (monthly)
P = principle of the loan (original loan amount)
i = interest rate (r) divided by 12 or simply r/12
n = number of months until payoff. 30 year mortgage = 12 months x 30 years = 360*** eHow doesn't allow exponent numbering so please look at this picture to see the real formula. It should read (1+i) to the nth power for example.
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USE SIMPLE NUMBERS TO UNDERSTAND THE MORTGAGE FORMULA.
Lets say the mortgage is 100,000 which is a relatively average number (127,500 being the average for the US in 2003). Let's also say we want to pay it off in 30 years (360 months) since that is the usual default. If the interest rate is very low at 5% then we have all we need to know. Start from the inside portions of the formula to move out.
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FIRST SOLVE FOR i AND REPLACE i WITH THE ANSWER IN THE MORTGAGE FORMULA
Working this out, i=r/12. So, the rate is .05. Divide that by twelve and you get .00416666667.
Now the mortgage formula reads M= P [ (1 + .00416666667)n ] / [ (1 + .00416666667)n - 1]*** Remember n is an exponent ... see picture.
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NEXT SOLVE FOR n.
This is easily done once you memorize a few numbers.
10 year mortgage = 120 months (10x12)
15 year mortgage = 180 months (15x12)
30 year mortgage = 360 months (30 x12)
40 year mortgage = 480 months (30 x 12)You usually only need to know the middle two, 180 and 360. In this example our formula reads like the attached picture (click to zoom).
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USE THE EXPONENT BUTTON ON A CALCULATOR TO SOLVE.
There is an online version of this function in the resource section below. Simply enter i+1 into the x box. Here that equals 1.004166667. Enter whatever the number of monthly payments is (360 here) and press enter. In this case it solves to be 4.4677444. Replace both parentheses that read (1+i) with that number. It should now read just like this:
M=P[.004166*4.4677444]/ [4.4677444-1]
Plug in the Principle (100k) and you can easily get the answer.
P*0053671782 = $536.70 monthly mortgage payment (excluding any escrow).
See resource section below for more help on mortgage payments.
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Tips & Warnings
Keep a simple excel version of this on file to speed up the process tremendously.
Resources
- Photo Credit (c) Jsolie l Dreamstime.com
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Comments
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I need to calculate interest rate.. any formula is there.. thanks..
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hello gud day. i am just wondering why 1 should be added to i in the formula for getting the mortgage. and also at the latter part of the formula, why is there n-1? why does 1 again is deducted from n? hope u'll find time to reply.thanks
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In general if you can't write exponents use the ^ symbol example 2^2 is two squared. Or M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1].
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thanks Ryan, would u please go slow, one by one, through a basic calculation, just with, say $200.000 for 30 years at 7% interest. i'm sorry i don't seem to understand that basics. thank you, margo,
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I have been in the mortgage business for 8+ years. I am very familliar with the mortgage process and how to assist in calculating payments. If you have questions give me a call at 866-295-9339 x 777. Ryan Salo Bank Of England. FDIC, Equal Housing Lender.
