Can someone please show me the math for how they work out a monthly mortgage payment?

Question

No matter how I try to calculate it, with interest, even with escrow and homeowner's insurance wrapped up, for a fixed rate 30-year-mortgage, I always get a way lower number than the bank. Where are they getting all the extra stuff that they add on? I just don't understand. Could you please do a sample 30-year-fixed at 6% with all the math shown?

Answer 1

Maybe the banks are having you pay PMI.  Private Mortgage Insurance.   If you don't have 20% down, that is probably what it is.

Answer 2

On a 100,000 loan P&I payments @ 6% would be: 599.55 or $6/thousand to estimate other loan amounts (good luck finding 6% without some good points).

Then you have to add in real estate taxes. On 100K, mine are $2,000/yr, but this varies widely from one area to another. Divide by 12 to get monthly or about $167.00.

Then you have home owners insurance. Mine runs $730/yr or $61/month.

Then you may have PMI if you borrower more than 80% of the value of the property. It could be .37% at 85%, .52% at 90%, .78% at 95% or .96% at 97%. FHA is about .55 at 97.75% on a purchase. These are annual factors. FHA premium on 100K would be about $46 monthly.

Add it all up:

Total PITI = $874 roughly.

I hope this helps.

Answer 3

Just google "mortgage calculator" and you'll find dozens -- probably hundreds -- of sites that will run those numbers for you, and you can see whether the results agree with you or with the bank.

Answer 4

Step 1.  Determine your periodic rate, Pr. For a monthly payment, that simply means dividing the annual interest rate (as a decimal) by 12. For instance, the monthly periodic rate for a loan with an interest rate of 6% is: Pr = .06 / 12 = .005

Step 2.  Add 1 to that number, or Pr + 1. In this case 1.005

Step 3.  Raise that number to the power of the total number of months. DON'T GET SCARED; it's not that bad. Your scientific calculator should have a y^x button. That would be a y with a small x on the upper right hand side of it.

So, if it was a 30 year mortgage, the number of payments would be 360. You would enter 1.005, hit the y^x button, then enter 360. The answer should be 6.022575212

Step 4.  You can either write that number down, or store it in memory #1, if your calculator supports that.

Step 5.  You next want to subtract 1 from that number, so that would be: 6.022575212 - 1 = 5.022575212

Step 6.  Divide the smaller number into the larger number:

6.022575212/5.022575212 = 1.19910105

Step 7.  Multiply 1.19910105 times the amount you want to borrow. Let's say it was 100,000, it would equal 119,910.105

Step 8.  Multiply 119,910.105 times the periodic rate Pr:

119,910.105 * .005 = 599.55

$599.55 would be your monthly mortgage payment for a $100,000 loan for 30 years at 6% annual interest.

Step 9.  In equation form, it looks like this:

Payment = (Pr+1)^#pmts. /((Pr+1)^#pmts.)-1) * Pr * Amount borrowed.

I wrote this exact example over at eHow, with a little more information added.