To calculate a mortgage payment for a fixed rate mortgage, where the interest rate never changes
there are four things you need to know. The principal, or the amount owed after the down
payment, the annual interest rate, the number of total years for the loan, and the number of
payments per year, which typically is once a month so 12 payments per year. The formula for
calculating the mortgage payment is the principal, times the quantity, annual percentage rate,
divided by the number of months in a year, times the quantity, one plus annual percentage rate,
divided by the number of months in a year. With this quantity raised to the number of months times
the total number of years of the loan, divided by the quantity, one plus the annual percentage rate,
divided by the number of months in a year, raised to the number of months, times the
number of years, minus one. And I shortened the formula using the symbols as you see here.
This formula may seem a bit intimidating but if you break it down it's much easier to work
with. So, let's say that after your down payment you're left owing two hundred thousand dollars,
which is your principle, the annual interest rate is four point five percent,
the loan is for thirty years, and there are twelve payments per year. In our formula we need to know
the annual percentage rate divided by the number of months in a year. Our annual percentage rate
is 4.5 percent which mathematically is 0.045 and the number of months is 12. So 0.045
divided by 12, which calculates out to 0.00375. Next in the formula we need to know one plus the
annual percentage rate, divided by the number of months in the year. We just calculated the
annual percentage rate divided by the number of months in a year. So this is one plus 0.00375,
which is 1.00375. Next we need to calculate this raised value
of the number of months times the number of years, which is 12 payments per year times 30 years,
which is 360. Next we can calculate this whole value of one plus annual percentage rate divided
by the number of months in a year, raised to the number of months times the number of years.
So we have 1.00375 raised to three hundred and sixty. If you recall when we raise some number to
a power such as two raised to the three, we just multiply that number times itself that many times.
So, two times two times two, which is eight. In our formula this is 1.00375 times itself
360 times. Using a calculator, or in excel, you would type in, equals 1.00375, carrot symbol,
which is shift 6 on the keyboard, 360. And the result is 3.847699, rounding it off. Now we have
everything in basic terms to plug and calculate into our formula. So, $200 000 times 0.00375,
times 3.847699, divided by 3.847699, minus one. And this calculates out to 1013.37, rounding off,
and that would be the monthly mortgage payment. There are also mortgage calculators online and
you can see here that using these numbers we get the same result. One thing to take note
of is the total cost of the loan, which is one thousand thirteen dollars and thirty seven cents,
times three sixty, the number of payments. And this gives us three hundred sixty four thousand
eight hundred thirteen dollars and twenty cents. If the interest rate was four point zero percent,
instead of four point five percent, this would result in a monthly payment of $957.83
and a total cost of $343,739 , so twenty one thousand seventy four dollars and 20 cents less.
And this is why the interest rate of any loan is so important to you, as a buyer. All right
my friends hopefully you got something out of this video, I do have more videos right there,
that you might have an interest in. Till next time I am out of here.