What’s in a Mortgage Payment Formula, Really?

What’s in a Mortgage Payment Formula, Really?

mortgage payment formula

Your mortgage payment: a set amount of money that is withdrawn from your account on a regular basis for years. Sure, you may just chalk it up to another large fixed expense. But understanding how your mortgage payment formula is calculated can help you make healthier financial decisions. So rather than just signing those mortgage papers and hoping for the best, take a gander at the story beneath those numbers…

Gathering the Basics 

Before you can start calculating your mortgage payment, you will need to collect the basic pieces of information. These are:

  1. The amount of your mortgage, also called the principal. This is the amount that you plan to borrow from your mortgage lender to buy your home.
  2. Your interest rate. This is how much you are being charged to borrow money. Note that this may not be the APR – that number includes closing costs. The interest rate does not.
  3. How long you have to pay the loan, sometimes called the term of the loan. This is usually in years.
  4. What kind of loan you have – fixed rate, adjustable rate, and so on.

Your Mortgage Payment Formula

Unfortunately, there isn’t a single mortgage payment formula to rule them all. Your formula depends on the type of loan you have. Considering that fixed rate loans are the most common type of mortgage, that is the one that will be used here.

Remember: A fixed rate loan means that that the interest rate, and therefore the mortgage payment, stays the same for the term of the mortgage.

Guess what? A mortgage payment formula means math time! So put on your thinking caps and let’s walk through this slowly. It isn’t nearly as bad as you think.

First, let’s start with an easy example:

  • You want to borrow $100,000 with a 6% interest rate for 30 years. Your payments will be monthly.

Next, your formula for a fixed rate mortgage is:

Loan Payment = Amount/Discount factor. That can also be written more simply as LP = A/D.

But there’s a little more to it than that. There are other values you need before you can start plugging numbers into your formula. Let’s get to those:

  1. The number of payments you will make each year, written as (n).
  2. Your interest rate, written as (i). This rate will be divided by the number of payments you make each year.
  3. The discount factor. A discount point is a one-time, upfront cost that lets you access discounted mortgage rates. Each discount point costs about 1% of your mortgage size. The discount factor formula is written as (D), where (D) =  {[(1 + i) ^n] – 1} / [i(1 + i)^n]. It looks worse than it actually is.

Hint: When a math equation looks imposing, break it down into smaller parts and start with what you know.

What do we know?

  • n = 12 payments per year x 30 years = 360.
  • i = 6% yearly interest rate (also written as .06) / your 12 monthly payments = .005.

Let’s plug those numbers into the discount factor equation:

D = {[(1 + .005) ^360] – 1} / [.005(1 + .05)^360]

D = 166.79

Now that we have the value for D, we can complete the mortgage payment formula. As stated earlier, it is:

LP = A/D

LP = 100,000/166.79

LP = 599.55 – which is your mortgage payment amount! Ta da!

Of course, doing it by hand can seem quite old school. Thankfully, there are plenty of online calculators like this one to help you do these calculations.

What About PMI?

Now, you may have noticed that a certain value was missing from the formula above – PMI. If you have less than a 20% down payment on your home, then you will need to pay PMI on top of your mortgage payment. Although fees can vary, PMI tends to range between 0.5% to 1% of your entire mortgage amount each year. So if your PMI is 1% on your $100,000 mortgage, you could be paying $1000 every year, or $83.33 each month. That’s on top of your mortgage payment.

Can You Afford a Home?

Just because a lender is willing a certain amount doesn’t mean you can necessarily afford that mortgage. Yes, your lender does use your financial details to determine how much they will lend you. But only you know all of your financial goals – retirement, vacations, a home renovation, college education, new car…and you get the idea.

To help you determine how much you are comfortable borrowing, use an personal budget worksheet. It lets you realize exactly how much income you have, and where that income is going. That will help you determine if you can afford a home, along with what else life has to offer.

Personal Budget Plan Download

Guest blog post by:

Nick Principe, Loan Officer with Shamrock Financial NMLS# 1537716

Ryan Rappoport, Sales Agent with Exit Realty

Seth Mintz, VP of Business Development with Equity National Title

 

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