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Nominal interest rate
In ﬁnance and economics,
nominal interest rate
or
nominalrateofinterest
referstotwodistinctthings: therate of interest before adjustment for inﬂation (in contrast
withtherealinterestrate); or, forinterestrates“asstated”without adjustment for the full eﬀect of compounding(also referred to as the
nominal annual rate
).
An in-terest rate is called
nominal
if the frequency of com-pounding (e.g. a month) is not identical to the
basictime unit
(normally a year).
1 Nominal versus real interest rate
The real interest rate is the nominal rate of interest minusinﬂation. In the case of a loan, it is this real interest thatthe lender receives as income. If the lender is receiving8 percent from a loan and inﬂation is 8 percent, then thereal rate of interest is zero because nominal interest andinﬂation are equal. A lender would have no net beneﬁtfrom such a loan because inﬂation fully diminishes thevalue of the loan’s proﬁt.The relationship between real and nominal interest ratescan be described in the equation:
(1 +
r
)(1 +
i
) = (1 +
R
)
where r is the real interest rate, i is the inﬂation rate, andR is the nominal interest rate.
[1]
ã
A common approximation for the real interest rateis:
real interest rate = nominal interest rate - ex- pected inﬂation
In thisanalysis, thenominal rateisthestated rate, and thereal interest rate is the interest after the expected lossesdue to inﬂation. Since the future inﬂation rate can onlybe estimated, the
ex ante
and
ex post
(before and after thefact)realinterestratesmaybediﬀerent;thepremiumpaidto actual inﬂation may be higher or lower. In contrast, thenominal interest rate is known in advance.
2 Nominal versus eﬀective interestrate
The nominal interest rate (also known as an AnnualisedPercentage Rate or APR) is the periodic interest ratemultiplied by the number of periods per year. For ex-ample, a nominal annual interest rate of 12% basedon monthly compounding means a 1% interest rate permonth(compounded).
[2]
Anominalinterestrateforcom-pounding periods less than a year is always lower than theequivalent rate with annual compounding (this immedi-ately follows from elementary algebraic manipulations ofthe formula for compound interest). Note that a nomi-nal rate without the compounding frequency is not fullydeﬁned: for any interest rate, the eﬀective interest ratecannot be speciﬁed without knowing the compoundingfrequency
and
the rate. Although some conventions areused where the compounding frequency is understood,consumers in particular may fail to understand the im-portance of knowing the eﬀective rate.Nominal interest rates are not comparable unless theircompounding periods are the same; eﬀective interestrates correct for this by “converting” nominal rates intoannual compound interest. In many cases, depending onlocal regulations, interest rates as quoted by lenders andin advertisements are based on nominal, not eﬀective in-terest rates, and hence may understate the interest ratecompared to the equivalent eﬀective annual rate.Confusingly, in the context of inﬂation, 'nominal' has adiﬀerent meaning. A nominal rate can mean a rate be-fore adjusting for inﬂation, and a real rate is a constant-prices rate. The FIsher equation is used to convert be-tween real and nominal rates. To avoid confusion aboutthe term nominal which has these diﬀerent meanings,someﬁnancetextbooksusetheterm'AnnualisedPercent-age Rate' or APR rather than 'nominal rate' when theyare discussing the diﬀerence between eﬀective rates andAPR’s.The term should not be confused with simple interest (asopposedtocompoundinterest)whichisnotcompounded.The eﬀective interest rate is always calculated as if com-pounded annually. The eﬀective rate is calculated in thefollowing way, where
r
is the eﬀective rate,
i
the nominalrate (as a decimal, e.g. 12% = 0.12), and
n
the numberof compounding periods per year (for example, 12 formonthly compounding):
r
= (1 +
i
/
n
)
n
−
1
3 Examples
1
2
5 EXTERNAL LINKS
3.1 Monthly compounding
Example1: Anominalinterestrateof6%/acompoundedmonthly is equivalent to an eﬀective interest rate of6.17%.Example 2: 6% annually is credited as 6%/12 = 0.5% ev-ery month. After one year, the initial capital is increasedby the factor (1+0.005)
12
≈ 1.0617.
3.2 Daily compounding
A loan with daily comp have a substantially higher ratein eﬀective annual terms. For a loan with a 10% nominalannual rate and daily compounding, the eﬀective annualrate is 10.516%. For a loan of $10,000 (paid at the endof the year in a single lump sum), the borrower wouldpay$51.56morethanonewhowascharged10%interest,compounded annually.
4 References
[1] Richard A. Brealey and Steward C. Meyer.
Principles of Corporate Finance,
Sixth Edition. Irwin McGraw-Hill,London, 2000. p. 49.[2] Charles Moyer, James R. McGuigan, William J. Kret-low.
Contemporary Financial Management
, Tenth Edi-tion. Thomson-South-Western, Mason, Ohio, 2006 pg.163.
5 External links
ã
Online Nominal Annual Interest Rate Calculator
ã
Online Interest Calculator
3
6 Text and image sources, contributors, and licenses
6.1 Text
ã
Nominal interest rate
Source:
http://en.wikipedia.org/wiki/Nominal_interest_rate?oldid=596510730
Contributors:
SimonP, Patrick,Guerby, Mkluwe, Rossami, Henrygb, Saturnight, Drbreznjev, SDC, SmackBot, Ohnoitsjamie, NickBall, Zven, PieRRoMaN, Hu12, Alejrb, Avillia, Rainer Bartoldus, Gregalton, PubliusFL, Magioladitis, Davidjk, Retail Investor, Obscurans, VolkovBot, SueHay, Lamro, Gka-pur, Egfrank, SieBot, Ham Pastrami, Emesee, Svick, Rinconsoleao, ClueBot, Uncle Milty, Jim 14159, Lucasgw8, Alexbot, DumZiBoT,Jurismedia, Addbot, Michaelm 22, Tide rolls, Qwertzy, Drilnoth, Mnmngb, Awhen, Île ﬂottante, Duoduoduo, Asweatherbee, Canyq,Yowchuan, WikitanvirBot, RA0808, ZéroBot, Jalehman37, ClueBot NG, Keithphw, Statoman71, Joshuajohnson555, Chris51659, An-drewkellyclan and Anonymous: 81
6.2 Images6.3 Content license
ã
Creative Commons Attribution-Share Alike 3.0

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