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In finance, accrued interest is the interest on a bond or loan that has accumulated since the principal investment, or since the previous coupon payment if there has been one already.
For a type of obligation such as a bond, interest is calculated and paid at set intervals (for instance annually or semi-annually). However ownership of bonds/loans can be transferred between different investors at any time, not just on an interest payment date. After such a transfer, the new owner will usually receive the next interest payment, but the previous owner must be compensated for the period of time for which he or she owned the bond. In other words, the previous owner must be paid the interest that accrued before the sale. This is generally done in one of two ways, depending on market convention:
On the other hand, if the sale is made during a short set period immediately before the next interest payment, then the seller, not the buyer, will receive the interest payment from the issuer of the loan (the borrower), and
In accounting, accrual-based accounting generally requires (in order to present a true and fair view) that accrued interest is computed and recorded at the end of each accounting period, perhaps by means of adjusting journal entries. This enables the accrued interest to be included in the lender's balance sheet as an asset (and in the borrower's balance sheet as a provision or liability). However if the accounts use the market price as derived by method 2 above, then such an adjustment for accrued interest is not necessary, as it has already been included in the market price.
The primary formula for calculating the interest accrued in a given period is:
where is the accrued interest, is the fraction of the year, is the principal, and is the annualized interest rate.
is usually calculated as follows:
where is the number of days in the period, and is the number of days in the year.
The main variables that affect the calculation are the period between interest payments and the day count convention used to determine the fraction of year, and the date rolling convention in use.
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
In finance, a bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to provide cash flow to the creditor. The timing and the amount of cash flow provided varies, depending on the economic value that is emphasized upon, thus giving rise to different types of bonds. The interest is usually payable at fixed intervals: semiannual, annual, and less often at other periods. Thus, a bond is a form of loan or IOU. Bonds provide the borrower with external funds to finance long-term investments or, in the case of government bonds, to finance current expenditure.
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.
In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with forward rate agreements (FRAs), and with zero coupon swaps (ZCSs).
In finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular it is a linear IRD with strong associations with interest rate swaps (IRSs).
In finance, an interest rate cap is a type of interest rate derivative in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed strike price. An example of a cap would be an agreement to receive a payment for each month the LIBOR rate exceeds 2.5%.
In finance, a futures contract is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price of the contract is known as the forward price. The specified time in the future when delivery and payment occur is known as the delivery date. Because it derives its value from the value of the underlying asset, a futures contract is a derivative.
A credit default swap (CDS) is a financial swap agreement that the seller of the CDS will compensate the buyer in the event of a debt default or other credit event. That is, the seller of the CDS insures the buyer against some reference asset defaulting. The buyer of the CDS makes a series of payments to the seller and, in exchange, may expect to receive a payoff if the asset defaults.
The yield to maturity (YTM), book yield or redemption yield of a bond or other fixed-interest security, such as gilts, is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. It is the (theoretical) internal rate of return : the discount rate at which the present value of all future cash flows from the bond is equal to the current price of the bond. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more often market convention is followed. In a number of major markets the convention is to quote annualized yields with semi-annual compounding ; thus, for example, an annual effective yield of 10.25% would be quoted as 10.00%, because 1.05 × 1.05 = 1.1025 and 2 × 5 = 10.
A repurchase agreement, also known as a repo, RP, or sale and repurchase agreement, is a form of short-term borrowing, mainly in government securities. The dealer sells the underlying security to investors and, by agreement between the two parties, buys them back shortly afterwards, usually the following day, at a slightly higher price.
Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the principal amount on maturity. Fixed-income securities — more commonly known as bonds — can be contrasted with equity securities – often referred to as stocks and shares – that create no obligation to pay dividends or any other form of income. Bonds carry a level of legal protections for investors that equity securities do not — in the event of a bankruptcy, bond holders would be repaid after liquidation of assets, whereas shareholders with stock often receive nothing.
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial term used in reference to bonds and other fixed-interest securities such as gilts. It is the ratio of the annual interest (coupon) payment and the bond's price:
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements (FRAs). This determines the number of days between two coupon payments, thus calculating the amount transferred on payment dates and also the accrued interest for dates between payments. The day count is also used to quantify periods of time when discounting a cash-flow to its present value. When a security such as a bond is sold between interest payment dates, the seller is eligible to some fraction of the coupon amount.
The price of a bond is the present value of its future cash-flows. To avoid the impact of the next coupon payment on the price of a bond, this cash flow is excluded from the price of the bond and is called the accrued interest. In finance, the dirty price is the price of a bond including any interest that has accrued since issue of the most recent coupon payment. This is to be compared with the clean price, which is the price of a bond excluding the accrued interest.
A mortgage loan or simply mortgage, in civil law jurisdictions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners to raise funds for any purpose while putting a lien on the property being mortgaged. The loan is "secured" on the borrower's property through a process known as mortgage origination. This means that a legal mechanism is put into place which allows the lender to take possession and sell the secured property to pay off the loan in the event the borrower defaults on the loan or otherwise fails to abide by its terms. The word mortgage is derived from a Law French term used in Britain in the Middle Ages meaning "death pledge" and refers to the pledge ending (dying) when either the obligation is fulfilled or the property is taken through foreclosure. A mortgage can also be described as "a borrower giving consideration in the form of a collateral for a benefit (loan)".
An asset swap refers to an exchange of tangible for intangible assets, in accountancy, or, in finance, to the exchange of the flow of payments from a given security for a different set of cash flows.
In finance, a zero coupon swap (ZCS) is an interest rate derivative (IRD). In particular it is a linear IRD, that in its specification is very similar to the much more widely traded interest rate swap (IRS).