# How Does the Bank Calculate My Monthly Payment?

Monthy Payment Calculator for
Auto Loans and Home Mortgages
Loan Period Length (months)
Annual Interest Rate (decimal)
Principal (amount borrowed)

You pay \$ per month.
Total interest paid: \$

Banks and mortgage calculators compute your monthly payments based on the annual interest rate, the period of the loan, and the principal. The formula they use is based on something called the "time value of money." It is a financial concept that means many things to lending institutions, but only one thing to a borrower: interest. Using the steps below you can learn to compute your monthly payments by hand, and be your own mortgage calculator. Or, to save time, you can use the mortgage calculator on the left. It works for both home loans and auto loans.

(Step 1) Express the annual interest rate as a decimal, and call this number R. For example, if the annual interest rate is 6%, then R = 0.06.

(Step 2) Multiply the number of years by 12 to find the number of months in the loan period. Call this number N. For example, if you have a 30 year mortgage, N = 360.

(Step 3) Compute the number (1+R/12)N and call this number W. Keep in mind that N is an exponent, so you need to use the xy button on your calculator, not the multiplication button. For example, if R = 0.06 and N = 360, then W = (1+.005)360 = 6.0226. Make sure you keep at least 4 digits behind the decimal point. If you round off too much, you will get an inaccurate final answer.

(Step 4) Call the principal of your loan P. Principal is another word for the amount borrowed when you take out a home loan or auto loan. It is the total cost of the house or vehicle minus any down payment you make.

(Step 5) Finally, compute the number (R/12)PW/(W-1). This number gives your monthly payment. For example, if the principal is \$100,000, you would pay (0.005)(100000)(6.0226)/(5.0226) = \$599.55 each month for 360 months.

You can also use these numbers to calculate the total interest you pay. Simply multiply the monthly payment by the number of months, and then subtract the loan principal. For example, (360)(599.55) = \$215,838, and \$215,838 - \$100,000 = \$115,838. So over the course of 360 months you will pay \$115,838 in interest fees.