exceed around 40% of total monthly pretax income. Some mortgage lenders are known to allow as high as 55%. Monthly payment formula The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures that the loan is paid off in full with interest at the end of its term. The monthly payment formula is based on the annuity formula. The monthly payment c depends upon: r - the monthly interest rate. Since the quoted yearly percentage rate is not a compounded rate, the monthly percentage rate is simply the yearly percentage rate divided by 12. For example, if the yearly percentage rate was 6% (i.e 0.06), then r would be or 0.5% (i.e 0.005). N - the number of monthly payments, called the loan's term, and P - the amount borrowed, known as the loan's principal. In the standardized calculations used in the United States, c is given by the formula: For example, for a home loan of $200,000 with a fixed yearly interest rate of 6.5% for 30 years, the principal is , the monthly interest rate is , the number of monthly payments is , the fixed monthly payment equals $1,264.14. This formula is provided using the financial function in a spreadsheet such as Excel. In the example, the monthly payment is obtained by entering either of these formulas: The following derivation of this formula illustrates how fixed-rate mortgage loans work. The amount owed on the loan at the end of every month equals the amount owed from the previous month, plus the interest on this amount, minus the fixed amount paid every month. This fact results in the debt schedule: The polynomial appearing before the fixed monthly payment c (with ) is a geometric series, which has a simple closed-form expression obtained from observing that because all but the first and last terms in this difference cancel each other out. Therefore, solving for yields the much simpler closed-form expression Applying this formula to the amount owed at the end of the Nth month gives (using to succinctly denote the function value at argument value ): The amount of the monthly payment at the end of month N that is applied to principal paydown equals the amount c of payment minus the amount of interest currently paid on the pre-existing unpaid principal. The latter amount, the interest component of