A mortgage calculator is an automated tool that enables the user to quickly determine the financial implications of changes in one or more variables in a mortgage financing arrangement. The major variables include loan principal balance, periodic interest rate compound interest, number of payments per year,total number of payments and the regular payment amount.
Mortgage calculator capability can be found on most financial calculators such as the HP-12C, in most desktop spreadsheet programs such as Microsoft Excel and on the Web.

Interest rates must be comparable in order to be useful, and in order to be comparable, the interest rate and the compounding frequency must be disclosed. Since most people think of rates as a yearly percentage, many governments require financial institutions to disclose a (notionally) comparable yearly interest rate on deposits or advances. Compound interest rates may be referred to as Annual Percentage Rate, Effective interest rate, Effective Annual Rate, and by other terms. When a fee is charged up front to obtain a loan, APR usually counts that cost as well as the compound interest in converting to the equivalent rate. These government requirements assist consumers to more easily compare the actual cost of borrowing.

Annual percentage rate (APR) is the simplified counterpart to the effective interest rate that the borrower will pay on a loan. In many countries and jurisdictions, lenders (such as banks) are required to disclose the cost of borrowing in some standardized way as a form of consumer protection. APR is intended to make it easier to compare lenders and loan options. The APR is likely to differ from the note rate or headline rate advertised by the lender, due to the addition of other fees that may need to be included in the APR. APRs can be found by asking the lender or by reading the appropriate section in the contract.

When purchasing a new home most buyers choose to finance a portion of the purchase price via the use of mortgage. Prior to the wide availability of mortgage calculators, those wishing to understand the financial implications of changes to the five main variables in a mortgage transaction were forced to use compound interest rate tables. These tables generally required a working understanding of compound interest mathematics for proper use. In contrast, mortgage calculators make answers to questions regarding the impact of changes in mortgage variables available to everyone.

In mathematics, the nth roots of unity, or de Moivre numbers, are all the complex numbers that yield 1 when raised to a given power n. They are located on the unit circle of the complex plane, and in that plane they form the vertices of an n-sided regular polygon with one vertex. 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. This monthly payment c depends upon the monthly interest rate (expressed as a fraction, not a percentage, i.e., divide the quoted yearly percentage rate by 100 and by 12 to obtain the monthly interest rate).

Note that neither the amounts nor the periods between transactions are necessarily equal. For the purposes of this calculation, a year is presumed to have 365 days (366 days for leap years), 52 weeks or 12 equal months. An equal month is presumed to have 30.41666 days regardless of whether or not it is a leap year. The result is to be expressed to at least one decimal place. This algorithm for APR is required for some but not all forms of consumer debt in the EU. For example, this EU directive is limited to agreements of 50,000 and below and excludes all mortgages.

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