*For the fees charged to merchants for accepting credit cards, see Discount Rate under Merchant Account.*
*For discount rate as a term in investment financing, see Discounted cash flow*

The

**discount rate** can mean

- an interest rate a central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...

charges depository institutionA depository institution is a financial institution in the United States that is legally allowed to accept monetary deposits from consumers...

s that borrow reservesBank reserves are banks' holdings of deposits in accounts with their central bank , plus currency that is physically held in the bank's vault . The central banks of some nations set minimum reserve requirements...

from it, for example for the use of the Federal Reserve's discount windowThe discount window is an instrument of monetary policy that allows eligible institutions to borrow money from the central bank, usually on a short-term basis, to meet temporary shortages of liquidity caused by internal or external disruptions...

.

- the same as interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

; the term "discount" does not refer to the common meaning of the word, but to the meaning in computations of present valuePresent value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...

, e.g. net present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

or discounted cash flowIn finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...

- the
*annual effective discount rate*, which is the annual interest divided by the capital including that interest; this rate is lower than the interest rate; it corresponds to using the value after a year as the nominal value, and seeing the initial value as the nominal value minus a discountDiscounts and allowances are reductions to a basic price of goods or services.They can occur anywhere in the distribution channel, modifying either the manufacturer's list price , the retail price , or the list price Discounts and allowances are reductions to a basic price of goods or services.They...

; it is used for Treasury Bills and similar financial instruments

## Annual effective discount rate

The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.

For example, suppose there is a

government bondA government bond is a bond issued by a national government denominated in the country's own currency. Bonds are debt investments whereby an investor loans a certain amount of money, for a certain amount of time, with a certain interest rate, to a company or country...

that sells for $95 and pays $100 in a year's time. The discount rate according to the given definition is

The interest rate is calculated using 95 as its base:

For every annual

effective interest rateThe 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...

, there is a corresponding annual effective discount rate, given by the following formula:

or inversely,

where the approximations apply for small

*i* and

*d*; in fact

*i* -

*d* =

*id*.

See also notation of interest rates.

## Business calculations

Businesses need to consider the discount rate when deciding whether to spend some of their profits on buying a new piece of equipment, or whether to give the profit back to their shareholders. In an ideal world, they would only buy a piece of equipment if the shareholders would get a bigger profit later. The amount of extra profit that a shareholder requires in the future in order to prefer that the company buy the equipment rather than giving them the profit now is based on the shareholder's discount rate. There is a widely used way of estimating shareholder's discount rates using share price data. It is known as the

capital asset pricing modelIn finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...

. Businesses normally apply this discount rate to their decisions about purchasing equipment by calculating the

net present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...

of the decision

## See also

- Discounting
- Social discount rate
Social discount rate is a measure used to help guide choices about the value of diverting funds to social projects. It is defined as "the appropriate value of r to use in computing present discount value for social investments"...

- Ramsey growth model
The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of economic growth based primarily on the work of the economist and mathematician Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans...

- Compare and contrast with federal funds
In the United States, federal funds are overnight borrowings by banks to maintain their bank reserves at the Federal Reserve. Banks keep reserves at Federal Reserve Banks to meet their reserve requirements and to clear financial transactions...

## External links