The terms annual percentage of rate (APR), nominal APR, and effective APR (EAR)[1] describe the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan A loan is a type of debt. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the lender and the borrower, mortgage, credit card A credit card is a small plastic card issued to users as a system of payment. It allows its holder to buy goods and services based on the holder's promise to pay for these goods and services. The issuer of the card grants a line of credit to the consumer from which the user can borrow money for payment to a merchant or as a cash advance to the, etc. It is a finance charge expressed as an annual rate. [2] Those terms have formal, legal definitions in some countries or legal jurisdictions Jurisdiction is the practical authority granted to a formally constituted legal body or to a political leader to deal with and make pronouncements on legal matters and, by implication, to administer justice within a defined area of responsibility. The term is also used to denote the geographical area or subject-matter to which such authority, but in general: [1]
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- The nominal APR is the simple-interest rate (for a year).
- The effective APR is the fee+compound interest Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal rate (calculated across a year).[1]
The nominal APR is calculated as: the rate, for a payment period, multiplied by the number of payment periods in a year.[1] However, the exact legal definition of "effective APR", or EAR in short, can vary greatly in each jurisdiction, depending on the type of fees included, such as participation fees, 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 through disbursal of funds . Loan servicing generally covers everything after disbursing the funds until the loan is fully paid off. Loan origination is a fees, monthly service charges A fee is the price one pays as remuneration for services. Fees usually allow for overhead, wages, costs, and markup, or late fees A late fee, also known as a late fine or a past due fee, is a charge levied against a client by a company or organization for not paying a bill or returning a rented or borrowed item by its due date. Its use is most commonly associated with businesses like creditors, video rental outlets and libraries. Late fees are generally calculated on a per. The effective APR has been called the "mathematically-true" interest rate for each year.[3][4] The computation for the effective APR, as the fee+compound interest Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal rate, can also vary depending on whether the up-front fees, such as origination or participation fees, are added to the entire amount, or treated as a short-term loan due in the first payment. When start-up fees are paid as first payment(s), the balance due might accrue more interest, as being delayed by the extra payment period(s).[5]
In some areas, the annual percentage rate (APR) is the simplified counterpart to the effective interest rate The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears. It is used to compare the annual interest between loans with different that the borrower will pay on a loan. When not using the term "effective APR", the use of "APR" is an early term for nominal APR. 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 Consumer protection laws are designed to ensure fair competition and the free flow of truthful information in the marketplace. The laws are designed to prevent businesses that engage in fraud or specified unfair practices from gaining an advantage over competitors and may provide additional protection for the weak and those unable to take care of. 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.
In the U.S. ^ b. English is the de facto language of American government and the sole language spoken at home by 80% of Americans age five and older. Spanish is the second most commonly spoken language and the UK The United Kingdom of Great Britain and Northern Ireland[note 7] is a sovereign state located off the northwestern coast of continental Europe. It is an island country, spanning an archipelago including Great Britain, the northeastern part of the island of Ireland, and many small islands. Northern Ireland is the only part of the UK with a land, lenders are required to disclose the APR before the loan (or credit application) is finalized (although the definition of "APR" is not the same in the two countries-–see below). Credit card companies can advertise monthly interest rates, but they are required to clearly state the annual percentage rate before an agreement is signed. APR is a term used with regard to deposit accounts as well. However, when dealing with deposit accounts, the annual percentage yield Annual percentage yield is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers (APY) or annual equivalent rate (AER) is quoted to consumers for comparison purposes.
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Multiple definitions of effective APR
There are at least three ways of computing effective annual percentage rate:
- by compounding the interest rate for each year, without considering fees;
- origination fees are added to the balance due, and the total amount is treated as the basis for computing compound interest;
- the origination fees An origination fee, or activation fee, is a payment associated with the establishment of an account with a bank, broker or other company providing services handling the processing associated with taking out a loan are amortized In computer science, especially analysis of algorithms, amortized analysis finds the average running time per operation over a worst-case sequence of operations. Amortized analysis differs from average-case performance in that probability is not involved; amortized analysis guarantees the time per operation over worst-case performance as a short-term loan. This loan is due in the first payment(s), and the unpaid balance is amortized as a second long-term loan. The extra first payment(s) is dedicated to primarily paying origination fees and interest charges on that portion.
For example, consider a $100 loan which must be repaid after one month, at 5% interest, plus a $10 fee. If the fee is neglected, this loan has a (year-long) effective APR of approximately 79% (1.05^12 =~1.7958). If the $10 fee were considered, the interest increases by 10% ($10/$100) for the month, with the effective APR being approximately 435% (1.15^12 =~5.3502, as 535%-100%=435%). Hence there are at least two possible "effective APRs": 79% and 435%.
Additional considerations
Confusion is possible in that if the word "effective" is used separately as meaning "influential" or having a "long-range effect", then the term effective APR will vary as being an expression, rather than a strict legal definition.
More confusion is possible in that when APR is treated as an abbreviation for the word "April" (4th month), then the term "effective APR" means "going into effect in April" (as a very common legal definition for the separate word "effective").
Still more confusion is possible in that the compound period affects the calculation of effective APR: for example, monthly compounding is different from daily compounding. Some credit cards A credit card is a small plastic card issued to users as a system of payment. It allows its holder to buy goods and services based on the holder's promise to pay for these goods and services. The issuer of the card grants a line of credit to the consumer from which the user can borrow money for payment to a merchant or as a cash advance to the compound interest daily [1] even though payments are due monthly. (See "Dependence on loan period", below.)
Rate format
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An effective annual interest rate The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears. It is used to compare the annual interest between loans with different of 10% can also be expressed in several ways:
- 0.7974% effective monthly interest rate, because 1.007974^12=1.1
- 9.569% annual interest rate compounded monthly, because 12*0.7974=9.569
- 9.091% annual rate in advance, because 1/1.1=1-0.091
These rates are all equivalent, but to a consumer who is not trained in the mathematics of finance The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will derive, and extend, the mathematical or numerical models suggested by financial economics. Thus, for example, while a financial economist might study the structural reasons why, this can be confusing. APR helps to standardize how interest rates are compared, so that a 10% loan is not made to look cheaper by calling it a loan at "9.1% annually in advance".
The APR does not necessarily convey the total amount of interest paid over the course of a year: if one pays part of the interest prior to the end of the year, the total amount of interest paid is less.
In the case of a loan with no fees, the amortization schedule An amortization schedule is a table detailing each periodic payment on an amortizing loan , as generated by an amortization calculator would be worked out by taking the principal left at the end of each month, multiplying by the monthly rate and then subtracting the monthly payment. This can be expressed mathematically by
- where:
- P0 is the initial principal
- r is the percentage rate used each payment
- n is the number of payments
This also explains why a 15 year mortgage and a 30 year mortgage with the same APR would have different monthly payments and a different total amount of interest paid. There are many more periods over which to spread the principal, which makes the payment smaller, but there are just as many periods over which to charge interest at the same rate, which makes the total amount of interest paid much greater. For example, $100,000 mortgaged (without fees, since they add into the calculation in a different way) over 15 years costs a total of $193,429.80 (interest is 93.430% of principal), but over 30 years, costs a total of $315,925.20 (interest is 215.925% of principal).
In addition the APR takes costs into account. Suppose for instance that $100,000 is borrowed with $1000 one-time fees paid in advance. If, in the second case, equal monthly payments are made of $946.01 against 9.569% compounded monthly then it takes 240 months to pay the loan back. If the $1000 one-time fees are taken into account then the yearly interest rate paid is effectively equal to 10.31%.
The APR concept can also be applied to savings accounts: imagine a savings account with 1% costs at each withdrawal and again 9.569% interest compounded monthly. Suppose that the complete amount including the interest is withdrawn after exactly one year. Then, taking this 1% fee into account, the savings effectively earned 8.9% interest that year.
Money factor
The APR can also be represented by a money factor (also known as the lease A lease is a contract calling for the lessee to pay the lessor (owner) for use of an asset. A rental agreement is a lease in which the asset is tangible property. Leases for intangible property could include use of a computer program (similar to a license, but with different provisions), or use of a radio frequency (such as a contract with a cell- factor, lease rate, or factor). The money factor is usually given as a decimal, for example .0030. To find the equivalent APR, the money factor is multiplied by 2400. A money factor of .0030 is equivalent to a monthly interest rate of 0.6% and an APR of 7.2%.[6]
For a leasing arrangement with an initial capital cost of C, a residual value at the end of the lease of F and a monthly interest rate of r, monthly interest starts at Cr and decreases almost linearly during the term of the lease to a final value of Fr.[7] The total amount of interest paid over the lease term of N months is therefore
and the average interest amount per month is
This amount is called the "monthly finance fee".[8] The factor r/2 is called the "money factor"
Failings
Despite repeated attempts by regulators to establish usable and consistent standards, APR does not represent the total cost of borrowing nor does it really create a comparable standard. Nevertheless, it is considered a reasonable starting point for an ad-hoc comparison of lenders.
Nominal APR does not reflect the true cost
Credit card holders should be aware that most U.S. credit cards are quoted in terms of nominal APR compounded monthly, which is not the same as the effective annual rate (EAR). Despite the “Annual” in APR, it is not necessarily a direct reference for the interest rate paid on a stable balance over one year. The more direct reference for the one-year rate of interest is EAR. The general conversion factor for APR to EAR is , where n represents the number of compounding periods of the APR per EAR period. As an example, for a common credit card quoted at 12.99% APR compounded monthly, the one year EAR is , or 13.7975%. For 12.99% APR compounded daily, the EAR paid on a stable balance over one year becomes 13.87% (see credit card interest Credit card interest is the principal way in which card issuers generate revenue. A card issuer is a bank that gives a consumer a card or account number that can be used with various payees to make payments and borrow money from the bank simultaneously. The bank pays the payee and then charges the cardholder interest over the time the money for the .000049 addition to the 12.99% APR). Note that a high U.S. APR of 29.99% compounded monthly carries an effective annual rate of 34.48%.
While the difference between APR and EAR may seem trivial, because of the exponential nature of interest these small differences can have a large effect over the life of a loan. For example, consider a 30-year loan of $200,000 with a stated APR of 10.00%, i.e., 10.0049% APR or the EAR equivalent of 10.4767%. The monthly payments, using APR, would be $1755.87. However, using an EAR of 10.00% the monthly payment would be $1691.78. The difference between the EAR and APR amounts to a difference of $64.09 per month. Over the life of a 30-year loan, this amounts to $23,070.86, which is over 11% of the original loan amount.
Certain fees are not considered
Some classes of fees are deliberately not included in the calculation of APR. Because these fees are not included, some consumer advocates claim that the APR does not represent the total cost of borrowing. Excluded fees may include:
- routine one-time fees which are paid to someone other than the lender (such as a real estate attorney's fee)
- penalties such as late fees or service reinstatement fees without regard for the size of the penalty or the likelihood that it will be imposed.
Lenders argue that the real estate attorney's fee, for example, is a pass-through cost, not a cost of the lending. In effect, they are arguing that the attorney's fee is a separate transaction and not a part of the loan. Consumer advocates argue that this would be true if the customer is free to select which attorney is used. If the lender insists on using a specific attorney however, then the cost should be looked at as a component of the total cost of doing business with that lender. This area is made more complicated by the practice of contingency fees – for example, when the lender receives money from the attorney and other agents to be the one used by the lender. Because of this, U.S. regulators require all lenders to produce an affiliated business disclosure form which shows the amounts paid between the lender and the appraisal firms, attorneys, etc.
Lenders argue that including late fees and other conditional charges would require them to make assumptions about the consumer's behavior – assumptions which would bias the resulting calculation and create more confusion than clarity.
Sat, 07 Aug 2010 14:14:19 GMT+00:00
: 5 Year ARM 2.75% MonitorBankRates.com Current 30 year mortgage rates are advertised at 4.50 percent with an annual percentage rate of 4.686 percent. Wells Fargo's 30 year mortgage rates are ...
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maintenance and depreciation costs are included in the savings Should my company purchase this machine given my cost of capital of 7 The answer is most probably yes since $500 000 would ordinarily generate only $3876 per month The maximum value of the machine should be $773 895
