# Dictionary Definition

interest

### Noun

1 a sense of concern with and curiosity about
someone or something; "an interest in music" [syn: involvement]

2 the power of attracting or holding one's
interest (because it is unusual or exciting etc.); "they said
nothing of great interest"; "primary colors can add interest to a
room" [syn: interestingness] [ant:
uninterestingness]

3 a reason for wanting something done; "for your
sake"; "died for the sake of his country"; "in the interest of
safety"; "in the common interest" [syn: sake]

4 a fixed charge for borrowing money; usually a
percentage of the amount borrowed; "how much interest do you pay on
your mortgage?"

5 a diversion that occupies one's time and
thoughts (usually pleasantly); "sailing is her favorite pastime";
"his main pastime is gambling"; "he counts reading among his
interests"; "they criticized the boy for his limited pursuits"
[syn: pastime, pursuit]

6 (law) a right or legal share of something; a
financial involvement with something; "they have interests all over
the world"; "a stake in the company's future" [syn: stake]

7 (usually plural) a social group whose members
control some field of activity and who have common aims; "the iron
interests stepped up production" [syn: interest
group]

### Verb

1 excite the curiosity of; engage the interest of
[ant: bore]

3 be of importance or consequence; "This matters
to me!" [syn: matter
to]

# User Contributed Dictionary

## English

### Noun

- A great attention and concern from someone or something.
- The price paid for obtaining, or price received for providing, money or goods in a credit transaction, calculated as a fraction of the amount or value of what was borrowed.
- Attention that is given to or received from someone or something.
- A business or
amorous link or involvement.
- I have business interests in South Africa.

#### Translations

great attention and concern from someone

- Czech: zájem
- Danish: interesse
- Dutch: interesse
- Esperanto: intereso
- Finnish: kiinnostus, mielenkiinto
- French: intérêt
- German: Interesse
- Hebrew: עניין
- Hindi: स्वारस्य (swaarasy)
- Hungarian: érdeklődés
- Indonesian: bunga (bank) kb, kepentingan kb, keuntungan kb
- Japanese: 興味, kyōmi}}, 関心, kanshin}}
- Korean: ,
- Kurdish: mereq, balkêşî, entres
- Malay: minat
- Malayalam: താല്പര്യം (thaalparyam)
- Marathi: (मराठी) स्वारस्य (swaarasy)
- Norwegian: interesse
- Polish: zainteresowanie
- Portuguese: interesse
- Romanian: interes
- Serbian: interes
- Spanish: interés
- Telugu: ఆసక్తి (aasakti)

the price of credit

- Czech: úrok
- Dutch: interest , rente v
- Esperanto: interezo
- Finnish: korko
- French: intérêt
- German: Zins
- Hebrew: ריבית
- Hindi: सूद (sood); ब्याज (byaaj)
- Hungarian: kamat
- Japanese: 利子, rishi}}, 利息, risoku}}
- Korean: ,
- Kurdish: faîz, riba
- Malay: bunga, faedah
- Malayalam: പലിശ (paliSa)
- Marathi: (मराठी) व्याज (vyaaj)
- Norwegian: rente
- Portuguese: juros
- Romanian: dobanda
- Serbian: interes
- Spanish: interés
- Telugu: వడ్డీ (vaDDEE)

attention that is given to or received from
someone or something

business or amorous link or involvement

- Chinese: 利益
- Hungarian: érdek
- Japanese: 利益
- Kurdish: entres
- Malay: kepentingan
- Portuguese: interesse
- Romanian: interes
- Serbian: interes
- Spanish: interés

- ttbc Esperanto: intereso or interesulo (4)

### Verb

#### Translations

to attract attention or concern

- Azeri: maraq
- Danish: interesserer
- Dutch: interesseren
- Esperanto: interesi
- Finnish: kiinnostaa
- German: interessieren
- Japanese: qualifier phrase 興味を引く
- Portuguese: interessar
- Spanish: interesar

## Latin

### Etymology

inflected form of interesse### Verb

interest- Active third-person singular indicative present form of interesse.

# Extensive Definition

Interest is a fee paid on borrowed capital.
Assets lent
include money, shares, consumer
goods through hire
purchase, major assets such as aircraft,
and even entire factories in finance
lease arrangements. The interest is calculated upon the value
of the assets in the same manner as upon money. Interest can be
thought of as "rent on
money".

The fee is compensation to the lender for
foregoing other useful investments that could have
been made with the loaned money. Instead of the lender using the
assets directly, they are advanced to the borrower. The borrower
then enjoys the benefit of using the assets ahead of the effort
required to obtain them, while the lender enjoys the benefit of the
fee paid by the borrower for the privilege. The amount lent, or the
value of the assets lent, is called the principal. This principal
value is held by the borrower on credit.
Interest is therefore the price of credit, not the price of money
as it is commonly - and mistakenly - believed to be. The percentage
of the principal that is paid as a fee (the interest), over a
certain period of time, is called the interest
rate.

## History of interest

Interest is the price paid for the use of savings over a given period of time. In the Middle Ages, time was considered to be property of God. Therefore, to charge interest was considered to commerce with God's property. Also, St. Thomas Aquinas, the leading theologian of the Catholic Church, argued that the charging of interest is wrong because it amounts to "double charging", charging for both the thing and the use of the thing. The church regarded this as a sin of usury; nevertheless, this rule was never strictly obeyed and eroded gradually until it disappeared during the industrial revolution. Some scholars think that banking started among Jewish families because of the restrictions of the church.... financial oppression of Jews tended to occur
in areas where they were most disliked, and if Jews reacted by
concentrating on money lending to gentiles, the unpopularity - and
so, of course, the pressure - would increase. This is that the Jews
became an element in a vicious circle. The Christians, on the basis
of the Biblical rulings, condemned interest-taking absolutely, and
from 1179
those who practiced it were excommunicated. But the
Christians also imposed the harshest financial burdens on the Jews.
The Jews reacted by engaging in the one business where Christian
laws actually discriminated in their favor, and so became
identified with the hated trade of moneylending.

Usury has always been
viewed negatively by the Roman Catholic Church. The Second
Lateran Council condemned any repayment of a debt with more
money than was originally loaned, the Council
of Vienna explicitly prohibited usury and declared any
legislation tolerant of usury to be heretical, and the first
scholastics reproved the charging of interest. In the medieval
economy, loans were entirely a consequence of necessity (bad
harvests, fire in a workplace) and, under those conditions, it was
considered morally reproachable to charge interest.

In the Renaissance
era, greater mobility of people facilitated an increase in commerce
and the appearance of appropriate conditions for entrepreneurs to start new,
lucrative businesses. Given that borrowed money was no longer
strictly for consumption but for production as well, it could not
be viewed in the same manner. The School of Salamanca elaborated
various reasons that justified the charging of interest. The person
who received a loan benefited and one could consider interest as a
premium paid for the risk taken by the loaning party. There was
also the question of opportunity
cost, in that the loaning party lost other possibilities of
utilizing the loaned money. Finally and perhaps most originally was
the consideration of money itself as merchandise, and the use of
one's money as something for which one should receive a benefit in
the form of interest.

Martín
de Azpilcueta also considered the effect of time. Other things
being equal, one would prefer to receive a given good now rather
than in the future. This preference
indicates greater value. Interest, under this theory, is the
payment for the time the loaning individual is deprived of the
money.

Economically, the interest rate is the cost of
capital and is subject to the laws of supply
and demand of the money
supply. The first attempt to control interest rates through
manipulation of the money supply was made by the French
Central Bank in 1847.

The first formal studies of interest rates and
their impact on society were conducted by Adam Smith,
Jeremy
Bentham and Mirabeau during
the birth of classic economic thought. In the early 20th century,
Irving
Fisher made a major breakthrough in the economic analysis of
interest rates by distinguishing nominal interest from real
interest. Several perspectives on the nature and impact of interest
rates have arisen since then. Among academics, the more modern
views of John
Maynard Keynes and Milton
Friedman are widely accepted.

Former Central President of the JUP Sahibzada
Fazal Karim MNA has stated that the Council of Islamic ideology
feels that Islamic
banking ought to be interest-free by
law.

## Types of interest

### Simple interest

Simple Interest is calculated only on the principal, or on that portion of the principal which remains unpaid.The amount of simple interest is calculated
according to the following formula:

- I_ = (r \cdot B_0) \cdot n

where r is the period interest rate (I/n), B0 the
initial balance and n the number of time periods elapsed.

To calculate the period interest rate r, one
divides the interest rate I by the number of periods n.

For example, imagine that a credit card holder
has an outstanding balance of $2500 and that the simple interest
rate is 12.99% per annum. The interest added at the end of 3 months
would be,

- I_ = \bigg(\frac\cdot $2500\bigg) \cdot 3=$81.19

and he would have to pay $2581.19 to pay off the
balance at this point.

If instead he makes interest-only payments for
each of those 3 months at the period rate r, the amount of interest
paid would be,

- I = \bigg(\frac\cdot $2500\bigg) \cdot 3= ($27.0625/month) \cdot 3=$81.19

His balance at the end of 3 months would still be
$2500.

In this case, the time
value of money is not factored in. The steady payments have an
additional cost that needs to be considered when comparing loans.
For example, given a $100 principal:

- Credit card debt where $1/day is charged: 1/100 = 1%/day = 7%/week = 365%/year.
- Corporate bond where the first $3 are due after six months, and the second $3 are due at the year's end: (3+3)/100 = 6%/year.
- Certificate of deposit (GIC) where $6 is paid at the year's end: 6/100 = 6%/year.

There are two complications involved when
comparing different simple interest bearing offers.

- When rates are the same but the periods are different a direct comparison is inaccurate because of the time value of money. Paying $3 every six months costs more than $6 paid at year end so, the 6% bond cannot be 'equated' to the 6% GIC.
- When interest is due, but not paid, does it remain 'interest payable', like the bond's $3 payment after six months or, will it be added to the balance due? In the latter case it is no longer simple interest, but compound interest.

### Compound interest

mainarticle Compound interest Compound interest is very similar to simple interest, however, as time goes on the difference becomes considerably larger. The conceptual difference is that unpaid interest is added to the balance due. Put another way, the borrower is charged interest on previous interest charges. Assuming that no part of the principal or subsequent interest has been paid, the debt is calculated by the following formulas:\begin
&I_=B_0\cdot\big[\left(1+r\right)^n-1\big]\\ &B_n=B_0+I_
\end

where Icomp is the compound interest, B0 the
initial balance, Bn the balance after n months and r the period
rate.

For example, if the credit card holder above
chose not to make any payments, the interest would accumulate

\begin &\mbox:\\
I_&=$2500\cdot\bigg[\bigg(1+\frac\bigg)^3-1\bigg]\\
&=$2500\cdot\left(1.010825^3-1\right)\\ &=$82.07\\
\end

\begin B_n&=B_0+I_\\ &=$2500+$82.07\\
&=$2582.07 \end

So, at the end of 3 months the credit card
holder's balance would be $2582.07 and he would now have to pay
$82.07 to get it down to the initial balance. Simple interest is
approximately the same as compound interest over short periods of
time so, more frequent payments is the better payment
strategy.

A problem with compound interest is that the
resulting obligation can be difficult to interpret. To simplify
this problem, a common convention in economics is to disclose the
interest rate as though the term were one year, with annual
compounding, yielding the effective
interest rate. However, interest rates in lending are often quoted as
nominal interest rates (i.e., compounding interest uncorrected
for the frequency of compounding). The discussion at compound
interest shows how to convert to and from the different
measures of interest.

Loans often include various non-interest charges
and fees. One example are points
on a mortgage
loan in the United States. When such fees are present, lenders
are regularly required to provide information on the 'true' cost of
finance, often expressed as an annual
percentage rate (APR). The APR attempts to express the total
cost of a loan as an interest rate after including the additional
fees and expenses, although details may vary by jurisdiction.

In economics,
continuous compounding is often used due to its particular
mathematical properties.

#### Fixed and floating rates

Commercial loans generally use compound interest, but they may not always have a single interest rate over the life of the loan. Loans for which the interest rate does not change are referred to as fixed rate loans. Loans may also have a changeable rate over the life of the loan based on some reference rate (such as LIBOR and EURIBOR), usually plus (or minus) a fixed margin. These are known as floating rate, variable rate or adjustable rate loans.Combinations of fixed-rate and floating-rate
loans are possible and frequently used. Less frequently, loans may
have different interest rates applied over the life of the loan,
where the changes to the interest rate are governed by specific
criteria other than an underlying interest rate. An example would
be a loan that uses specific periods of time to dictate specific
changes in the rate, such as a rate of 5% in the first year, 6% in
the second, and 7% in the third.

### Composition of interest rates

In economics, interest is considered the price of money, therefore, it is also subject to distortions due to inflation. The nominal interest rate, which refers to the price before adjustment to inflation, is the one visible to the consumer (i.e., the interest tagged in a loan contract, credit card statement, etc). Nominal interest is composed by the real interest rate plus inflation, among other factors. A simple formula for the nominal interest is:i= r + \pi

Where i is the nominal interest, r is the real
interest and \pi is inflation.

This formula attempts to measure the value of the
interest in units of stable purchasing power. However, if this
statement was true, it would imply at least two misconceptions.
First, that all interest rates within an area that shares the same
inflation (i.e. the same country) should be the same. Second, that
the lender knows the inflation for the period of time that he/she
is going to lend the money.

One reason behind the difference between the
interest that yields a
Treasury bond and the interest that yields a Mortgage
loan is the risk that the lender takes from lending money to an
economic agent. In this particular case, the US government is more
likely to pay than a private citizen. Therefore, the interest rate
charged to a private citizen is larger than the rate charged to the
US government.

To take into account the information
asymmetry aforementioned, both the value of inflation and the
real price of money is changed to their expected values resulting in
the following equation:

i_t = r_ + \pi_ + \sigma

Where i_t is the nominal interest at the time of
the loan, r_ is the real interest expected over the period of the
loan, \pi_ is the inflation expected over the period of the loan
and \sigma is the representative value for the risk engaged in the
operation.

### Cumulative interest or return

Cumulative interest/return: This calculation is (FV/PV)-1. It ignores the 'per year' convention and assumes compounding at every payment date. It is usually used to compare two long term opportunities. Since the difference in rates gets magnified by time, so the speaker's point is more clearly made.### Other conventions and uses

Other exceptions:- US and Canadian T-Bills (short term Government debt) have a different convention. Their interest is calculated as (100-P)/P where 'P' is the price paid. Instead of normalizing it to a year, the interest is prorated by the number of days 't': (365/t)*100. (See also: Day count convention). The total calculation is ((100-P)/P)*((365/t)*100). This is equivalent to calculating the price by a process called discounting at a simple interest rate.
- Corporate Bonds are most frequently payable twice yearly. The amount of interest paid is the simple interest disclosed divided by two (multiplied by the face value of debt).

Flat Rate Loans and the Rule of 78s: Some
consumer loans have been structured as flat rate loans, with the
loan outstanding determined by allocating the total interest across
the term of the loan by using the "Rule of
78s" or "Sum of digits" method. Seventy-eight is the sum of the
numbers 1 through 12, inclusive. The practice enabled quick
calculations of interest in the pre-computer days. In a loan with
interest calculated per the Rule of 78s, the total interest over
the life of the loan is calculated as either simple or compound
interest and amounts to the same as either of the above methods.
Payments remain constant over the life of the loan; however,
payments are allocated to interest in progressively smaller
amounts. In a one-year loan, in the first month, 12/78 of all
interest owed over the life of the loan is due; in the second
month, 11/78; progressing to the twelfth month where only 1/78 of
all interest is due. The practical effect of the Rule of 78s is to
make early pay-offs of term loans more expensive. For a one year
loan, approximately 3/4 of all interest due is collected by the
sixth month, and pay-off of the principal then will cause the
effective interest rate to be much higher than the APY used to
calculate the payments. http://www.bankrate.com/brm/news/auto/20010827a.asp

In 1992, the United
States outlawed the use of "Rule of 78s" interest in connection
with mortgage refinancing and other consumer loans over five years
in term. Certain other jurisdictions have outlawed application of
the Rule of 78s in certain types of loans, particularly consumer
loans. http://www.bankrate.com/brm/news/auto/20010827a.asp

Rule of 72: The "Rule of 72"
is a "quick and dirty" method for finding out how fast money
doubles for a given interest rate. For example, if you have an
interest rate of 6%, it will take 72/6 or 12 years for your money
to double, compounding at 6%. This is an approximation that starts
to break down above 10%.

## Market interest rates

There are markets for investments which include the money market, bond market, as well as retail financial institutions like banks, which set interest rates. Each specific debt takes into account the following factors in determining its interest rate:Opportunity
cost: This encompasses any other use to which the money could
be put, including lending to others, investing elsewhere, holding
cash (for safety, for example), and simply spending the
funds.

Inflation: Since the lender is deferring his
consumption, he will at a bare minimum, want to recover enough to
pay the increased cost of goods due to inflation. Because future
inflation is unknown, there are three tactics.

- Charge X% interest 'plus inflation'. Many governments issue 'real-return' or 'inflation indexed' bonds. The principal amount and the interest payments are continually increased by the rate of inflations. See the discussion at real interest rate.
- Decide on the 'expected' inflation rate. This still leaves both parties exposed to the risk of 'unexpected' inflation.
- Allow the interest rate to be periodically changed. While a 'fixed interest rate' remains the same throughout the life of the debt, 'variable' or 'floating' rates can be reset. There are derivative products that allow for hedging and swaps between the two.

Default: There is always the risk the borrower
will become bankrupt, abscond or otherwise default on the loan. The
risk premium attempts to measure the integrity of the borrower, the
risk of his enterprise succeeding and the security of any
collateral pledged. For example, loans to developing countries have
higher risk premiums than those to the US government due to the
difference in creditworthiness. An operating line of credit to a
business will have a higher rate than a mortgage.

Creditworthiness of businesses is measured by
bond rating services and individual's credit
scores by credit bureaus. The risks of an individual debt may
have a large standard deviation of possibilities. The lender may
want to cover his maximum risk. But lenders with portfolios of debt
can lower the risk premium to cover just the most probable
outcome.

Deferred consumption: Charging interest equal
only to inflation will leave the lender with the same purchasing
power, but he would prefer his own consumption NOW rather than
later. There will be an interest premium of the delay. See the
discussion at time value of money. He may not want to consume, but
instead would invest in another product. The possible return he
could realize in competing investments will determine what interest
he charges.

Length of time: Time has two effects.

- Shorter terms have less risk of default and inflation because the near future is easier to predict. Broadly speaking, if interest rates increase, then investment decreases due to the higher cost of borrowing (all else being equal).

Interest rates are generally determined by the
market, but government intervention - usually by a central
bank- may strongly influence short-term interest rates, and is
used as the main tool of monetary
policy. The central bank offers to buy or sell money at the
desired rate and, due to their control of certain tools (such as,
in many countries, the ability to print money) they are able to
influence overall market interest rates.

Investment can change rapidly to changes in
interest rates, affecting national income, and, through Okun's Law,
changes in output affect unemployment.

### Open market operations in the United States

The Federal Reserve (often referred to as 'The Fed') implements monetary policy largely by targeting the federal funds rate. This is the rate that banks charge each other for overnight loans of federal funds. Federal funds are the reserves held by banks at the Fed.Open
market operations are one tool within monetary policy
implemented by the Federal Reserve to steer short-term interest
rates. Using the power to buy and sell treasury securities, the Open Market
Desk at the
Federal Reserve Bank of New York can supply the market with
dollars by purchasing T-notes, hence increasing the nation's money
supply. By increasing the money supply or Aggregate Supply of
Funding (ASF), interest rates will fall due to the excess of
dollars banks will end up with in their reserves. Excess reserves
may be lent in the Fed funds
market to other banks, thus driving down rates.

### Interest rates and credit risk

It is increasingly recognized that the business cycle, interest rates and credit risk are tightly interrelated. The Jarrow-Turnbull model was the first model of credit risk which explicitly had random interest rates at its core. Lando (2004), Darrell Duffie and Singleton (2003), and van Deventer and Imai (2003) discuss interest rates when the issuer of the interest-bearing instrument can default.### Money and inflation

Loans, bonds, and shares have some of the characteristics of money and are included in the broad money supply.By setting i*n, the government institution can
affect the markets to alter the total of loans, bonds and shares
issued. Generally speaking, a higher real interest rate reduces the
broad money supply.

Through the quantity
theory of money, increases in the money supply lead to
inflation. This means that interest rates can affect inflation in
the future.

## Interest in mathematics

Jacob Bernoulli discovered the mathematical constant e by studying a question about compound interest.He realized that if an account that starts with
$1.00 and pays 100% interest per year, at the end of the year, the
value is $2.00; but if the interest is computed and added twice in
the year, the $1 is multiplied by 1.5 twice, yielding
$1.00×1.5² = $2.25. Compounding
quarterly yields
$1.00×1.254 = $2.4414…, and so on

Bernoulli noticed that this sequence can be
modeled as follows:

- \lim_ \left(1+\dfrac\right)^n=e,

where n is the number of times the interest is to
be compounded in a year.

## Formulas and Worksheets

The balance
of a loan with regular monthly payments is augmented by the monthly
interest charge and decreased by the payment so,

- B_=\big(1+r\big)B_k-p.

where,

- i = loan rate/100 = annual rate in decimal form (e.g. 10% = 0.10 The loan rate is the rate used to compute payments and balances.)
- r = period rate = i/12 for monthly payments (customary usage for convenience)http://www.fdic.gov/regulations/laws/rules/6500-1650.html#6500226.14
- B0 = initial balance (loan principal)
- Bk = balance after k payments
- k = balance index
- p = period (monthly) payment

By repeated substitution one obtains expressions
for Bk which are linearly proportional to B0 and p and use of the
formula for the partial sum of a geometric
series results in,

- B_k=(1+r)^k B_0 - \frac\ p

A solution of this expression for p in terms of
B0 and Bn reduces to,

- p=r\Bigg[\frac+B_0\Bigg]

To find the payment if the loan is to be paid off
in n payments one sets Bn = 0.

The PMT function found in spreadsheet programs can be
used to calculate the monthly payment of a loan:

- p=PMT(rate,num,PV,FV,) = PMT(r,n,-B_0,B_n,)\;

An interest-only payment on the current balance
would be,

- p_I=r B\;

The total interest, IT, paid on the loan
is,

- I_T=np-B_0\;

The formulas for a regular savings program are
similar but the payments are added to the balances instead of being
subtracted and the formula for the payment is the negative of the
one above. These formulas are only approximate since actual loan
balances are affected by rounding. In order to avoid an
underpayment at the end of the loan the payment needs to be rounded
up to the next cent. The final payment would then be
(1+r)Bn-1.

Consider a similar loan but with a new period
equal to k periods of the problem above. If rk and pk are the new
rate and payment, we now have,

- B_k=B'_0=(1+r_k)B_0-p_k\;

Comparing this with the expression for Bk above
we note that,

- r_k=(1+r)^k-1\;
- p_k=\frac r_k

The last equation allows us to define a constant
which is the same for both problems,

- B^*=\frac=\frac

and Bk can be written,

- B_k=(1+r_k)B_0-r_k B^*\;

Solving for rk we find a formula for rk involving
known quantities and Bk, the balance after k periods,

- r_k=\frac

Since B0 could be any balance in the loan, the
formula works for any two balances separate by k periods and can be
used to compute a value for the annual interest rate.

B* is a scale
invariant since it doesn't change with changes in the length of
the period.

Rearranging the equation for B* one gets a
transformation coefficient (scale
factor),

- \lambda_k=\frac=\frac=\frac=k[1+\frac+\cdots] (see binomial theorem)

and we see that r and p transform in the same
manner,

- r_k=\lambda_k r\;
- p_k=\lambda_k p\;

The change in the balance transforms
likewise,

- \Delta B_k=B'-B=(\lambda_k rB-\lambda_k p)=\lambda_k \Delta B \;

which gives an insight into the meaning of some
of the coefficients found in the formulas above. The annual rate,
r12, assumes only one payment per year and is not an "effective"
rate for monthly payments. With monthly payments the monthly
interest is paid out of each payment and so should not be
compounded and an annual rate of 12·r would make more sense. If one
just made interest-only payments the amount paid for the year would
be 12·r·B0.

Substituting pk = rk B* into the equation for the
Bk we get,

- B_k=B_0-r_k(B^*-B_0)\;

Since Bn = 0 we can solve for B*,

- B^*=B_0\bigg(\frac+1\bigg)

Substituting back into the formula for the Bk
shows that they are a linear function of the rk and therefore the
λk,

- B_k=B_0\bigg(1-\frac\bigg)=B_0\bigg(1-\frac\bigg)

This is the easiest way of estimating the
balances if the λk are known. Substituting into the first formula
for Bk above and solving for λk+1 we get,

- \lambda_=1+(1+r)\lambda_k\;

λ0 and λn can be found using the formula for λk
above or computing the λk recursively from λ0 = 0 to λn.

Since p=rB* the formula for the payment reduces
to,

- p=\bigg(r+\frac\bigg)B_0

and the average interest rate over the period of
the loan is,

- r_=\frac=r+\frac-\frac

which is less than r if n>1.

## See also

- Rate of return on investment
- Cash accumulation equation
- Credit rating agency
- Credit card interest
- Discount
- Fisher equation
- Hire purchase
- Leasing
- Monetary policy
- Mortgage loan
- Risk-free interest rate
- Yield curve
- Time value of money
- Usury
- Simple Interest
- Riba
- JAK members bank a Swedish interest-free bank

## References

### Specific references

### General references

- Credit Risk: Pricing, Measurement, and Management
- The Theory of Interest
- Credit Risk Modeling: Theory and Applications
- Credit Risk Models and the Basel Accords

## External links

interest in Bulgarian: Лихва

interest in Bosnian: Kamata

interest in German: Zins

interest in Modern Greek (1453-): Τόκος

interest in Esperanto: Interezo

interest in Spanish: Interés

interest in Estonian: Intress

interest in Persian: بهره (پول)

interest in Finnish: Korko

interest in French: Intérêt

interest in Hebrew: ריבית

interest in Croatian: kamata

interest in Hungarian: Kamat

interest in Indonesian: Suku bunga

interest in Italian: Interesse

interest in Japanese: 利子

interest in Korean: 이자

interest in Lao: ດອກເບ້ຍ

interest in Lithuanian: Palūkanos

interest in Dutch: Rente

interest in Norwegian: Rente

interest in Polish: Odsetki

interest in Portuguese: Juro

interest in Russian: процентная ставка

interest in Albanian: Interesi

interest in Serbian: Камата

interest in Swedish: Ränta

interest in Thai: ดอกเบี้ย

interest in Turkish: Faiz

interest in Chinese: 利息

# Synonyms, Antonyms and Related Words

absolute interest, absorb, absorption, accent, accrued dividends,
accumulated dividends, acquisitiveness,
activities, activity, advantage, advocacy, aegis, affair, affairs, affect, affect the interest,
agacerie, allotment, allowance, allure, allurement, amusement, animate, answer to, appeal, appertain to, applicability, application, apply to,
appositeness,
appurtenance,
arouse, attention, attentiveness, attract, attraction, attractiveness, auspices, authority, autism, avail, avocation, aye, backing, bag, bait, bank rate, be attractive,
bear on, bear upon, bearing, beckon, beguilement, beguiling, behalf, behoof, belong to, benefit, benison, bewitchery, bewitchment, bias, big end, bigger half,
birthright, bit, bite, blandishment, blessing, boon, breakaway group, bribe, bring, budget, business, cajolery, camp, campaign, capital gains,
captivate, captivation, capture, care, careerism, carrot, carry, cash dividend, catch, catch up in, cathexis, caucus, cause, championship, charisma, charity, charm, charmingness, chunk, claim, cleanup, clear profit,
come-hither, commerce,
commission, commitment, common, compensatory interest,
compound interest, con,
concern, concernment, conjugal right,
connect, connection, consequence, consequentiality,
consideration,
contingent,
contingent interest, convenience, correspond to,
countenance,
crusade, cumulative
dividend, curiosity,
curious mind, curiousness, cut, deal, deal with, decide, demand, destiny, determine, discount rate,
discrimination,
dispose, diversion, dividend, dividends, divine right,
division, doing, dole, drag, draw, draw in, drive, droit, due, earnings, easement, ego trip, egotism, embarrass, emphasis, employ, employment, enchantment, encouragement, end, engage, engagement, engross, engrossment, enlist, enmesh, entangle, enterprise, entertainment, enthrallment, enthusiasm, enticement, entrapment, equal share,
equitable interest, equity, estate, ethnic group, excellence, excite, excite interest, excitement, exorbitant
interest, extra dividend, faction, faculty, faith, fascinate, fascination, fate, favor, favoritism, fetch, fillip, filthy lucre, fire, flirtation, forbidden fruit,
fosterage, function, gain, gains, germaneness, get, get to do, gettings, ghoulishness, glamour, gleanings, good, goodwill, graspingness, great cause,
greed, gross, gross interest, gross
profit, guidance,
half, halver, have connection with,
helping, high order,
high rank, hoard, hobby, hold, holding, implicate, import, importance, inalienable
right, incentive,
incite, incitement, inclination, incline, income, individualism, induce, inducement, inequality, infect, influence, inquiring mind,
inquisitiveness,
inside track, interest group, interest in, interest rate, interestedness, interests, interim dividend,
intrigue, inveiglement, investment, invitation, invite, involve, involve in, involvement, issue, itch for knowledge,
job, killing, kindle, labor, lead, leaning, liaise with, lifework, limitation, link with, lively
interest, lookout,
lot, lucrative interest,
lucre, lure, magnetism, makings, mark, mass movement, materiality, matter, matter of interest,
measure, meddlesomeness, meed, melon, mental acquisitiveness,
merit, mess, minority group, modicum, moiety, moment, morbid curiosity,
mortgage points, move,
movement, narcissism, natural right,
nay, neat profit, nepotism, net, net interest, net profit,
no, nosiness, note, notice, occupation, officiousness, offshoot, one-sidedness,
optional dividend, paper profits, paramountcy, part, parti pris, partiality, participation, partisanism, partisanship, party, passion, pastime, patronage, payment, pelf, penal interest, percentage, perk, perks, perquisite, personal aims,
personal ambition, personal desires, personalism, persuade, persuasive, pertain to,
pertinence, phony
dividend, pickings,
piece, pique, plaque, plum, point, political party, portion, possessiveness, power, precedence, preeminence, preference, preferential
treatment, premium,
prerogative,
prescription,
pressure group, presumptive right, pretense, pretension, prevail upon,
price, price of money,
primacy, principle, priority, privatism, pro, proceeding, proceeds, procure, profit, profits, prompt, proper claim, property, property right,
proportion, prosperity, provocation, provoke, prurience, prurient interest,
prying, pull, pursuit, quantum, quicken, quota, rake-off, rate, rate of interest, ration, reason for being,
receipts, refer to,
reference, regard, regular dividend, relate
to, relatedness,
relaxation, relevance, remoteness, respect, return, returns, reward, right, right of entry, scopophilia, scrutiny, seconding, sect, seducement, seduction, seductiveness, segment, self-absorption,
self-admiration, self-advancement, self-centeredness,
self-consideration, self-containment, self-devotion, self-esteem,
self-importance, self-indulgence, self-interest,
self-interestedness, self-jealousy, self-occupation, self-pleasing,
self-seeking, self-serving, self-solicitude, self-sufficiency,
selfishness,
selfism, service, settlement, sex appeal,
share, side, significance, silent
majority, simple interest, slice, small share, snare, snaring, special dividend,
special favor, special interest, splinter, splinter group,
sponsorship,
stake, stimulate, stimulation, stimulative, stimulus, stock, stock dividend, store, stress, strict settlement, suck
into, suction, summon, superiority, supremacy, sway, sweetener, sweetening, sympathy, take, take-in, talk into, tangle, tantalization, tantalize, tease, tempt, temptation, the affirmative,
the negative, thing,
thirst for knowledge, tickle, tie in with, titillate, title, touch, touch upon, transaction, treat of,
trust, tutelage, undertaking, undetachment, undispassionateness,
unneutrality,
use, usury, value, vested interest, vested
right, vocal minority, voyeurism, wealth, weight, welfare, well-being, whet, whet the appetite, wing, winning ways, winnings, winsomeness, witchery, wooing, work, world of good, worth