The Effective Mortgage Payment formula estimates the average monthly cost of a tax deductible mortgage for the first year of a loan.  The formula takes into consideration the tax break for interest payments on home mortgages.

Inputs

• L - the Principal loan amount
• n - the number of months in the duration of the loan
  • n = 360 for a 30 year loan
  • n = 180 for a 15 year loan
  • n = 120 for a 10 year loan
• i - the annual interest rate entered as a percentage
• T - the tax rate assumed

Description

The Effective Payment algorithm first calculates the 

1. monthly payment, the 
2. amount of interest paid in the first year, and then 
3. uses the entered tax rate to calculate an Effective Payment amount that reflects the out-of-pocket payments for the first year of a loan, including the tax deduction for interest paid on some loans (e.g. home loan).

Usage

This calculator is useful, because it can help a first time home owner better estimate their cash flow burden in the first year of a mortgage.  There are numerous benefits to owning a home.  The first and obvious benefit is the building of equity in the property with every contribution towards the principal loan amount and with all appreciation in the value of the property.  A second and significant benefit is that many governments allow home owners to deduct the interest paid on a primary (and sometimes secondary) residence as a tax deduction.  This deduction has the effect of reducing taxes, especially in the early period of a mortgage when the interest portion of a loan is the highest.

This function calculates the monthly payment on a loan based on principal, interest rate and duration of the loan (e.g. $100,000 at 4.5% across 20 years).  This function then calculates how much of the loan payments in the first year are interest payments, which is the tax deductible amount.   It then calculates the tax benefit based on the user's approximate income tax rate (e.g. 33%).  Finally, this function spreads that tax benefit across the first year and calculates an Effective Monthly payment (Monthly Payment - Monthly tax benefit). 

How to manage personal cash flow

One can wait for their tax return to get back the tax money associated with one's home mortgage.  However, many people in the U.S. will increase the number of personal deductions used in tax withholding in their regular pay checks when they buy a home.  This can effectively negate or lessen the annualized effect of the mortgage interest deduction.