What Formulas Are Used to Calculate Mortgages?
Formulas are used at every stage of the mortgage process--in determining how much money you can borrow, what your monthly payment will be, how much of that monthly payment will be interest, how much money you will have to pay over the life of the loan, and what the effective interest rate will be.
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Front End Ratio
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The front end ratio measures bases your maximum monthly mortgage payment on your monthly income level. Most lenders do not allow the monthly payment to be more than 28 percent of your monthly income. If your monthly income were $5,000, your mortgage payment could not be more than $1,400.
Back End Ratio
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The back end ratio compares your total debt payments to your monthly income. Your total debt payments can include credit card debt, student loans and car loans in addition to your mortgage payment. Most lenders do not allow your total debt payments to exceed 36 percent of your monthly income. If your monthly income is $5,000, your total debt payments for the month could not exceed $1,800. If you are already paying $1,000 per month for your auto loan, your monthly mortgage payment could not be greater than $800.
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Monthly Mortgage Payment
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To calculate your monthly mortgage payment, use the following formula in which M is the monthly mortgage payment, P is the principal of the loan, R is the monthly rate and N is the number of payments.
M = P ( R (1 + R) ^ N ) / ((1 + R) ^ N - 1)
Make sure that you use the monthly rate rather than the annual rate. To determine the monthly rate, divide the annual rate by twelve.
Effective Interest Rate
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The effective interest rate is different from the stated interest rate, because the interest on the mortgage is usually compounded more than once a year. Many mortgages have the interest compounded each month.
Effective Interest Rate = ( 1 + I / N ) ^ N - 1
For example, if you signed a mortgage at 7 percent compounded monthly, or 12 times per year, the effective interest rate would be 7.23 percent.
Total Cost of the Loan
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To determine the total cost of the loan, multiple the number of payments by the amount of each monthly payment. For example, if you took out a $200,000 mortgage as a 30-year loan at 6 percent interest, your monthly payment would be $1,199.10. Since you would be making 360 payments, the total cost of the loan would be $431,676--$200,000 in principal and $231,676 in interest.
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