Have you ever wondered how the bank calculates your monthly mortgage payments? Perhaps you’d like to know how to do it yourself so the next time you go house hunting you know how much you can afford. There is a specific formula to follow and I’m willing to show you, but before we get into that you’ll need to know how interest is charged on a mortgage. In the banking industry it’s called compounded interest.
Compounded interest in most cases works on an annual basis. For instance, if you borrowed $1,000 at 5% annually for 10 years, your first year’s interest would be $50.00. If your total payments for the first 12 months added up to $150.00, you would have paid that year’s interest plus the additional $100.00 towards what you borrowed. The interest for the second year would then be based on the remaining $900 in principle, making it $45.00. After the second year, the amount payed toward the principle is deducted and interest re-calculated; this process would continue for the life of the loan.
In a nutshell, compounded interest is calculated using the total amount of principle still owed at the beginning of each year. Because of this formula, on a standard 30 year mortgage, the payments for the first ten years or so are almost exclusively eaten up by interest. The only way to get ahead and avoid some of that interest is to pay extra against the principle as often as possible.
Now for the formula: M = P [ i(1 + i)n ] / [ (1 + i)n - 1]
What… you don’t understand? Step into my data room and let me do my best to explain it to you.
M = the monthly mortgage payment; it’s what we’re trying to figure out. i = the annual interest rate divided by 12 (we divide by twelve because you are taking the total interest and spreading it out over 12 monthly payments). n = the total number of payments (12 months times 15 years would be 180 payments). So, on an $80,000 mortgage at 5% for 15 years we’ll start by calculating the annual interest rate (i):
i = 0.05 / 12 or 0.004167 and n = 12 x 15 or 180 monthly payments
We calculate (1 + i)n as: 1+ 0.004167 to the 180th power which equals 2.11383. Plugging these numbers into the formula gives us: M = P [ i(2.11383)] / [ 2.11383- 1], where P = the principle of the loan. Using our high school algebra skills we end up with a simplified equation of M = P [.004167 x 2.11383] / 1.11383 or M = $80,000 x 0.00790. The mortgage payment works out to $632 per month. Of course, don’t forget to add in your taxes, insurance and PMI if applicable.
Are you still confused? Well today’s your lucky day, because there’s an easier way to calculate your mortgage if you’re interested. Just do a web search on the phrase “calculate a mortgage”. You’ll have access to hundreds of websites that will do it for free!
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