Have a student loan, home loan, or personal loan? Have you ever wondered exactly how your lender calculated your monthly payment on the day you accepted the money? Sure, there are interest calculators and other available resources online to help you figure out just how much you will be paying back at the end of a loan, but sometimes it’s useful to figure it out for yourself.
Assume you are the proud owners of a new home and you need to finance a total of $250,000 over a 30 year fixed mortgage rate of five percent. Do you know what your monthly payment will be? Do you know how much money you are going to pay over the course of the full 30 years? Sadly, the numbers are probably a lot bigger than you think, but I’m going to show you just how to calculate this information on your own.
The formula for figuring out your own monthly payment on a principal loan is as follows:
M = P x J / 1 – (1 + J) ^ -N
To solve this formula, let’s first define all of the variables:
- M = Your monthly loan payment
- P = The principal amount of the loan. In this case, $250,000
- I = The annual interest rate. In this case, 5%
- L = Length in years of the loan. In this case, 30
- J = Interest rate in decimal form. (I / (12×100), in this case, 0.004166666667
- N = Number of months the loan is good for (L x 12). In this case, 360
Now that we have everything defined, a few simple computations and we will figure out just how much our monthly payment will be. Make sure you follow your math rules, always taking care of things in parenthesis first, then exponents, multiplication, division, addition and finally subtraction.
M = 250,000 x 0.00416666666667 / 1 – (1.00416666666667) ^ (-360)
Computing the number raised to the power of (-360) then subtracting it from 1, our formula is simplified and looks as follows:
M = 250,000 x 0.00416666666667 / 0.776173399
The final step is dividing the two numbers and multiplying the result by the principal balance of $250,000. Our results show a monthly payment of $1,342.05, which is exactly what any mortgage calculator will show if you use the above criteria. When you multiply this monthly payment over the course of 360 months, you find out that a total of $483,138 will be paid on a $250,000 loan. YIKES!
At anytime during your mortgage or loan, you usually have the option of paying more than you owe for the month, thereby reducing your principal. Paying off a little extra early on can save you thousands over the course of your entire loan and figuring out your new monthly payment is just as simple. Just change the principal amount and the number of months remaining on the loan to figure out what your new monthly payment will be.
And that’s all there is to calculating how much your monthly payment will be on a fixed interest rate loan. It’s never a pretty number in the end, but of course you can always make extra payments to reduce how long you take to repay the loan (and how much interest you pay).