Accrued Interest Calculator

Introduction

Accrued interest is the amount that accumulates on a bond or other debt security over a specific period (i.e., between coupon dates). It is the interest that has been earned but has not yet been paid to the bondholder or creditor. You can calculate the Accrued Interest using our Accrued Interest Calculator.

Accrued Interest is used to calculate the Dirty Price of the Bond, where $\text{Dirty Price = Clean Price + Accrued Interest}$

Clean Price is the price of the bond at the time of the most recent coupon payment.

How is Accrued Interest Calculated?

Using the Accrued Interest Calculator, we can calculate the accrued interest by specifying the following parameters

Issue date: The date when the security was issued.

First Interest date: Date of first interest of the security.

Settlement date: Security settlement date is when the seller trades the security to the buyer. The settlement date will always be after the issue date.

Coupon rate: Security’s annual coupon rate.

Par value: The security’s par value.

Frequency: Number of coupon payments paid in a year – usually annually, semi-annually, or quarterly.

Basis: Day count basis used for calculation.

Options are:

Basis
US (NASD) 30/360
Actual / Actual
Actual / 360
Actual / 365
European 30 / 360

Day Count Basis

Calculation Method → This option is used to specify whether the total accrued interest is calculated from the first interest date to the settlement date or from the issue date to the settlement date.

All the variables must have a value for the accrued interest calculator to calculate the answer.

Day Count Conventions

The accrued interest calculator allows you to set the day count basis. Day count conventions are standard practices for calculating the number of days between two dates.

Day Count conventions are used for calculating the Accrued Interest, where we need to find the days between the previous coupon date and the value date.

We use the following day count conventions to calculate the number of days between two dates.

Actual / Actual

Most bonds, like treasury coupon securities, use the Actual / Actual day count convention, where the actual number of days in a month and the actual number of days in the coupon period are used for the calculations.

But there are different day count conventions where the accrued interest might vary.

Actual / 360

Actual / 360 is a Day Count Convention where the accrued interest is given by multiplying the coupon rate with the actual number of days and dividing by 360.

\text{Accrued \;Interest = Coupon\; Rate}\times \normalsize \dfrac{\text{Days}}{360}

Actual / 365

Actual / 365 is a Day Count Convention where the accrued interest is given by multiplying the coupon rate with the actual number of days and dividing by 365.

\text{Accrued \;Interest = Coupon\; Rate}\times \normalsize \dfrac{\text{Days}}{365}

The accrued interest calculated with the Actual / 360 day count convention will be slightly more than the interest calculated by the Actual / Actual or the Actual / 365 method.

US (NASD) 30/360

In the US (NASD) 30/360 day count convention regardless of the number of days in a month, we consider that there are 30 days, and irrespective of the number of days in a year we consider that there are 360 days in a year.

To Calculate the Day Count:

Start Date: M1/D1/Y1

End Date: M2/D2/Y2

If $D_1 = 31$ , we set $D_1 = 30$

If $(D_2 = 31)$ and $(D_1 = 30\; \text{or}\; 31)$ , then we set $D_2 = 30$

\text{Day Count} = (Y_2 - Y_1)\times360 + (M_2 - M_1)\times30+(D_2-D_1)

\text{Day Count Fraction} = \normalsize \dfrac{\text{Day Count}}{360}

European 30/360

In the European 30/360 day count convention regardless of the number of days in a month, we consider that there are 30 days and irrespective of the number of days in a year we consider that there are 360 days in a year.

To Calculate the Day Count:

Start Date: M1/D1/Y1

End Date: M2/D2/Y2

If $(D_2 = 31)$ , then we set $D_2 = 30$

\text{Day Count} = (Y_2 - Y_1)\times360 + (M_2 - M_1)\times30+(D_2-D_1)

\text{Day Count Fraction} = \normalsize \dfrac{\text{Day Count}}{360}

The 30 / 360 Day Count conventions are the easiest conventions to use and they were primarily used before the advent of calculators or computers for easy calculation of the number of days between the coupon date and the value date.

Day Count Conventions used in US Bond Markets

Bond Market	Day Count Basis
US Treasury Notes	Actual / Actual
Money Market Instruments	Actual / 360
Corporate, Agency, and Municipal Bonds	30 / 360

Day Count Conventions used in US Bond Markets

Bond Markets outside of the US use the Actual/Actual convention except the following

Bond Market	Day Count Basis
Eurobonds	30 / 360
Denmark, Sweden, Switzerland	30E / 360
Norway	Actual / 365

Conventions in other markets

Now, if you want to know more about Bonds and Bond Pricing read on.

What are Bonds?

A bond is a debt instrument; the bond buyer lends money to the issuer and expects the borrowed amount to be repaid with interest, and most bonds pay regular interest until they mature.

The interest paid is the compensation the borrower provides to the lender for lending them the money.

Governments, corporations, or agencies issue bonds, which can be publicly placed (anyone can buy them) or privately placed (sold only to a select few investors). Bonds can be secured using collateral or maybe unsecured.

Key Features of Bonds

Maturity

Generally, It is the date on which the borrower will repay the principal, and the bond will cease. The bondholder can expect to receive coupon interest in the period in between. The bond buyer can sell the bond to another buyer before maturity, but the bond price may vary.

The yield of a bond depends heavily on the bond’s maturity.

The price of the bond will vary depending upon maturity. For example, if the interest rates changes, the effect of the change will be more drastic on the price of a bond with a shorter maturity than that of a bond with a long maturity.

Face Value

The face value also referred to as the par value of a bond, is the amount repaid to the investor at maturity.

Coupon Rate

The interest rate the borrower must pay the bondholders during the bond term.

We get the coupon payments that we pay to the bondholders by multiplying the coupon rate and the par value or face value.

Frequency

The issuer makes the coupon payments periodically, which will be monthly, quarterly, semiannually, or annually. These terms will be specified during the issue of the bond. Typically, In the United States, the coupon payment is made semiannually. In European bond markets, coupon payment is often annual.

Yield

the yield of a bond is the annualized return of a bond, expressed as the percentage of invested capital.

A bond’s yield depends upon its price, coupon rate, and amount paid at maturity.

Nominal Yield

The nominal yield is another name for the coupon rate of the bond. The stated interest rate is calculated as a percentage of the par value.

A bond with a $1000 par value that pays 5% interest semiannually will pay out $25 payments every six months totaling $50 at the end of the year, so the nominal yield will be $50 / $1000 = 5%.

\text{Nominal Yield}= \normalsize \dfrac{\text{Annual Interest Payment}}{\text{Par Value}}

The price of the bond and the interest rates are inversely related if interest rates rise the bond prices will decline and if the interest rates fall the bond prices will rise.

So, when the price of a bond changes the yield or the return of the bond will also change.

Current Yield

The buyer can approximate the bond’s yield by calculating the current yield of the bond, by dividing the annual coupon payment by the bond price.

\text{Current Yield} = \normalsize \dfrac{\text{Annual Coupon Payment}}{\text{Current Market Price of Bond}}

True Yield or Yield-to-Maturity (YTM)

Yield-to-Maturity (YTM) is the return on the bond if you hold it till maturity.

Mathematically, it is the discount rate at which the sum of the present value of all future cash flows from coupon payments as well as the principal repayment, equals the price of the bond.

When you buy a bond at a discount the YTM will exceed the current yield and if you buy the bond at a premium the YTM will be less than the current yield.

\text{Price} = \sum_{t-1}^T \normalsize \dfrac{\text{Cash Flows}}{(1 + YTM)^t}

Where YTM = Yield-to-Maturity

How are Bonds Priced?

Generally, the price of a financial instrument will be equal to the present value of the expected future cash flows.

The same logic applies to bonds as well the price of the bonds will be equal to the present value of future cash flows such as the interest payments as well as the principal repayment at maturity.

\text{Bond\;Price} = PV(\text{Coupon}_1) + PV(\text{Coupon}_2)+...+PV(\text{Coupon}_n)+PV(\text{Principal})

The bond price above is the clean price. You can use the bond price calculator to calculate the bond price.

The following factors determine the bond prices

The Face value or Par value.
The coupon rate.
Accrued interest.
Prevailing interest rates in the market.
Credit rating of the issuer.

When the bond is issued they generally sold at par which is the amount that has to be repaid at maturity. During the bond’s life, due to interest rate fluctuations and supply and demand changes, the bond’s price may vary. It can sell higher or lower than par.

When the interest rate rises the bond prices decline and when the interest rate falls the bond prices rise.

The bond price also will include the accrued interest, which is the interest you earn between the coupon payment dates and the interest earned but not paid. You can calculate this value using the accrued interest calculator at the top of the page.

Clean bond prices are bond prices without the accrued interest and dirty prices will include the accrued interest.

\text{Clean\;Bond\;Price} = \normalsize \dfrac{C_1}{(1+\dfrac{r}{k})^1} + \dfrac{C_2}{(1+\dfrac{r}{k})^2} + ... + \dfrac{C_n}{(1+\dfrac{r}{k})^{kn}} + \dfrac{P}{(1+\dfrac{r}{k})^{kn}}

Where

C = Coupon Payment

k = Frequency of Coupon Payments in a Year

n = Number of Years until maturity

r = Annualised Interest Rate

P = Par/Face Value of Bond

Bond’s Dirty Price

The dirty price of the bond is equal to the clean price plus the accrued interest.

\text{Dirty Price = Clean Price + Accrued Interest}

Where you can calculate the Accrued Interest as

\text{Accrued Interest} = \text{Interest Payment} *( \normalsize \dfrac{\text{Days since last payment}}{\text{Days between Payments}})