Interest rate

The interest rate, even rate of return, is the interval, expressed as a percentage rate for a capital loan, so the interest rate as a percentage, for example, for the rent.

• 2.1 General interest formula
• 2.2 basis of the interest rate i
• 2.3 Bank Year: practices of the units of time t / T
• 2.4 compound interest: Annual and continuous interest rate

• 3.1 Fixed rate and variable rate
• 3.2 Internal Rate of Return
• 3.3 Discount rate

Size symbols

In which employing interest rate and interest rates literature we find both the description and the name i r. Since, however, now internationally the term i appears to enforce this term is used here.

Distinction between interest rate and rate of return

Sometimes p and interest rate is precise distinction between interest rate i. The rate of interest is then the number before the % sign, at an interest rate of 8% is therefore p = 8 In contrast, i = 8 % = 8/ 100 = 0.08.

It is therefore:

Calculation methods

General interest formula

With

Tax base of the interest rate i

Usually the interest rate is based on one year ( p. a, ​​per annum / per annum). In addition, monthly interest rates are also p. M. per mese and those of the quarter ( p. Qu ) ago.

Bank Year: practices of the units of time t / T

For correct use of the interest formula t with respect to days and days divisor T is always an indication of the interest calculation method important. These practices are called generally the Bank year.

The Calculation method specifies how to proceed with maturities of less than one year. There are the following methods:

• 30/360 ( German method): The year is expected to be 360 days, every month ever with 30 days
• Act/360 ( € method or the French Usance ): The year is expected to be 360 days, the month include the actual days ( actual, German klm, calendar- ')
• Act/365 ( English method): The year is counted as calendar excessive common year of 365 days, the month include the actual days ( actual)
• Act / act ( the-day method): Both the year and month are calculated with the actual days ( actual). The Interest Period will be divided when leap years are included, and for each part of the corresponding splitters are used. (Example: December 20, 2007 until January 20, 2008: 31 days, divided into 11 days / 365 and 20 days / 366)

On the money markets in the euro area, the method is now act/360 usual.

Normally, the first day ( the date on which the interest rate business ) is not miteingerechnet.

Serves as an example of an interest rate i = 5 % = 0.05 and a capital sum from k = 100,000.00 euros. The money will be February 15, 2008 to March 15, 2008 applied ( a leap year ) (Appendix recording so on February 14, 2008). This result for the interest calculation methods following interest payments:

• 30/360:

• Act/360:

• Act/365:

• Act / act:

Compound interest: Annual and continuous interest rate

The influence of compounding effect on the result is a simple calculation:

Each of continuous compounding interest rate corresponds to an interest rate compounded annually ( p. a ) according to the following formula:

An annual interest rate of 20 % corresponds to a continuous interest rate of 18.23 %.

For periods that differ by a year, it's often cheaper to expect interest rates in continuous compounding. Hours Exact calculation is not common in the banking industry.

Types of interest rates

There are different types of interest rates, for example:

• Nominal Interest Rate: pure interest rate at which the interest amount is calculated
• Real interest rate: the interest rate adjustment to the effects of inflation
• Effective interest rate: involvement of disbursement rate, service charges and interest payments unterperiodigen

Basic interest rates in the overall economy are key interest rate for interbank loans, and Eckzinssatz for savings.

Fixed rate and variable rate

Under fixed-rate refers to the interest rate that remains unchanged constant for a certain period of time, regardless of the current market rate developments. A legal definition provides § 489 para 5 of the Civil Code, which is a " bound " interest rate for the entire contract period as a fixed percentage agreed. A fixed rate can be agreed either for the whole term of the loan or investment or only for a portion of the term ( see mortgage term ). A variable interest rate is conformal to the current market situation interest. Are inadmissible for contracts with variable interest rate arbitrary shapes. Rather, it is contractually set a reference interest rate, which takes into account the individual contracts and is available in the public media. Here, the time series database of the Deutsche Bundesbank offers.

Internal rate of return

The internal rate of return is the interest rate at which the net present value of a payment or series of a project by definition is exactly zero. This suggests that using the internal rate of return method to determine whether the implementation of this project or is not advantageous. Advantage - and therefore a positive net present value sourcing - the project is always when the discount rate is lower than the internal rate unfavorably in the case when the discount rate is higher. Also called effective interest rate (used in financing) or Internal Rate of Return ( IRR).

Discount rate

The discount rate or discount rate ( hurdle rate engl. or required rate of return ) is used in the statement of investments in discounted cash flow analysis. It refers to the subjective minimum return requirement of an investor on his investment and determines how strongly devalued further payments to occur in future to their present value. The discount is determined by the cost of capital or weighted average cost of capital for a risk premium increases (investment ) or decreased ( lending ) are.

Taking into account the time value of money is clear that the demand for a high return is equivalent to the demand for risky and short-term investments, as near present- payments are valued more than the later.