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Mortgage calculators are automated tools that enable users to determine the financial implications of changes in one or more variables in a
mortgage A mortgage loan or simply mortgage (), in civil law (legal system), civil law jurisdictions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners t ...
financing arrangement. Mortgage calculators are used by consumers to determine monthly repayments, and by mortgage providers to determine the financial suitability of a home loan applicant. Mortgage calculators are frequently on for-profit websites, though the Consumer Financial Protection Bureau has launched its own public mortgage calculator. The major variables in a mortgage calculation include loan principal, balance, periodic
compound interest Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compo ...
rate, number of payments per year, total number of payments and the regular payment amount. More complex calculators can take into account other costs associated with a mortgage, such as local and state taxes, and insurance. Mortgage calculation capabilities can be found on financial handheld calculators such as the
HP-12C The HP-12C is a financial calculator made by Hewlett-Packard (HP) and its successor HP Inc. as part of the HP Voyager series, introduced in 1981. It is HP's longest and best-selling product and is considered the '' de facto standard'' among fin ...
or
Texas Instruments Texas Instruments Incorporated (TI) is an American multinational semiconductor company headquartered in Dallas, Texas. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog ...
TI BA II Plus. There are also multiple free online free mortgage calculators, and software programs offering financial and mortgage calculations.


Uses

When purchasing a new home, most buyers choose to finance a portion of the purchase price via the use of a 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 Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compo ...
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. Mortgage calculators can be used to answer such questions as: If one borrows $250,000 at a 7% annual interest rate and pays the loan back over thirty years, with $3,000 annual property tax payment, $1,500 annual property insurance cost and 0.5% annual private mortgage insurance payment, what will the monthly payment be? The answer is $2,142.42. A potential borrower can use an online mortgage calculator to see how much property he or she can afford. A lender will compare the person's total monthly income and total monthly debt load. A mortgage calculator can help to add up all income sources and compare this to all monthly debt payments. It can also factor in a potential
mortgage A mortgage loan or simply mortgage (), in civil law (legal system), civil law jurisdictions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners t ...
payment and other associated housing costs (
property taxes A property tax (whose rate is expressed as a percentage or per mille, also called ''millage'') is an ad valorem tax on the value of a property.In the OECD classification scheme, tax on property includes "taxes on immovable property or net we ...
, homeownership dues, etc.). One can test different loan sizes and interest rates. Generally speaking, lenders do not like to see all of a borrower's debt payments (including property expenses) 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 A fixed-rate mortgage (FRM) is a mortgage loan where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or "float". As a result, payment amounts and the duration of ...
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 An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the 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 0.06/12 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 In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...
: For example, for a home loan of $200,000 with a fixed yearly interest rate of 6.5% for 30 years, the principal is P=200000, the monthly interest rate is r=0.065/12, the number of monthly payments is N=30\cdot 12=360, the fixed monthly payment equals $1,264.14. This formula is provided using the financial function in a
spreadsheet A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in c ...
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 In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
p_N(x)=1+x+x^2+ \cdots +x^ appearing before the fixed monthly payment ''c'' (with x=1+r) is a
geometric series In mathematics, a geometric series is a series (mathematics), series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, 1/2 + 1/4 + 1/8 + 1/16 + ⋯, the series \tfrac12 + \tfrac1 ...
, which has a simple
closed-form expression In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. ...
obtained from observing that xp_N(x)-p_N(x)=x^N-1 because all but the first and last terms in this difference cancel each other out. Therefore, solving for p_N(x) yields the much simpler
closed-form expression In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. ...
Applying this formula to the amount owed at the end of the ''N''th month gives (using p_N to succinctly denote the function value p_N(x) at argument value x = (1+r)): 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 the current payment, is the interest rate ''r'' times the amount unpaid at the end of month ''N''–1. Since in the early years of the mortgage the unpaid principal is still large, so are the interest payments on it; so the portion of the monthly payment going toward paying down the principal is very small and equity in the property accumulates very slowly (in the absence of changes in the market value of the property). But in the later years of the mortgage, when the principal has already been substantially paid down and not much monthly interest needs to be paid, most of the monthly payment goes toward repayment of the principal, and the remaining principal declines rapidly. The borrower's equity in the property equals the current market value of the property minus the amount owed according to the above formula. With a
fixed rate mortgage A fixed-rate mortgage (FRM) is a mortgage loan where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or "float". As a result, payment amounts and the duration of ...
, the borrower agrees to pay off the loan completely at the end of the loan's term, so the amount owed at month ''N'' must be zero. For this to happen, the monthly payment ''c'' can be obtained from the previous equation to obtain: which is the formula originally provided. This derivation illustrates three key components of fixed-rate loans: (1) the fixed monthly payment depends upon the amount borrowed, the interest rate, and the length of time over which the loan is repaid; (2) the amount owed every month equals the amount owed from the previous month plus interest on that amount, minus the fixed monthly payment; (3) the fixed monthly payment is chosen so that the loan is paid off in full with interest at the end of its term and no more money is owed.


Adjustable interest rates

While adjustable-rate mortgages have been around for decades, from 2002 through 2005 adjustable-rate mortgages became more complicated as did the calculations involved. Lending became much more creative which complicated the calculations. Subprime lending and creative loans such as the "pick a payment", "pay option", and "hybrid" loans brought on a new era of mortgage calculations. The more creative adjustable mortgages meant some changes in the calculations to specifically handle these complicated loans. To calculate the
annual percentage rate The term annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mort ...
s (APR) many more variables needed to be added, including: the starting interest rate; the length of time at that rate; the recast; the payment change; the index; the margins; the periodic interest change cap; the payment cap; lifetime cap; the
negative amortization In finance, negative amortization (also known as NegAm, deferred interest or graduated payment mortgage) occurs whenever the loan payment for any period is less than the interest charged over that period so that the outstanding balance of the lo ...
cap; and others. Many lenders created their own software programs, and World Savings even had contracted special calculators to be made by Calculated Industries specifically for their "pick a payment" program. However, by the late 2000s the
Great Recession The Great Recession was a period of market decline in economies around the world that occurred from late 2007 to mid-2009.
brought an end to many of the creative "pick-a-payment" type of loans which left many borrowers with higher loan balances over time, and owing more than their houses were worth. This also helped reduce the more complicated calculations that went along with these mortgages.


Total interest paid formula

The total amount of interest I that will be paid over the lifetime of the loan is the difference of the total payment amount (cN) and the loan principal (P): where c is the fixed monthly payment, N is the number of payments that will be made, and P is the initial principal balance on the loan. The cumulative interest paid at the end of any period N can be calculated by:


Outside the U.S.

In the United Kingdom, the FCA - Financial Conduct Authority (formerly the FSA - Financial Services Authority) regulates loans secured on residential property. It does not prescribe any specific calculation method. However, it does prescribe that, for comparative purposes, lenders must display an Annual Percentage Rate as prominently as they display other rates. In Spain, the regulatory authority ( Banco de España) has issued and enforced some good practices, such as clearly advertising the Annual Percentage Rate and stating how and when payments change in variable rate mortgages.


See also

* Bridge financing *
Financing Funding is the act of providing resources to finance a need, program, or project. While this is usually in the form of money, it can also take the form of effort or time from an organization or company. Generally, this word is used when a firm use ...
*
Fixed rate mortgage A fixed-rate mortgage (FRM) is a mortgage loan where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or "float". As a result, payment amounts and the duration of ...
* Adjustable-rate mortgage *
Mortgage loan A mortgage loan or simply mortgage (), in civil law (legal system), civil law jurisdictions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners t ...
*
Promissory note A promissory note, sometimes referred to as a note payable, is a legal instrument (more particularly, a financing instrument and a debt instrument), in which one party (the ''maker'' or ''issuer'') promises in writing to pay a determinate sum of ...
*
Loan origination Loan origination is the process by which a borrower applies for a new loan, and a lender processes that application. Origination generally includes all the steps from taking a loan application up to disbursal of funds (or declining the applicatio ...
* Subprime lending


References


External links


Mortgage Calculator
at NYTimes.com {{DEFAULTSORT:Mortgage Calculator Accounting software Mortgage