Bond Calculator – Calculate Bond Prices and Yields
Estimate bond prices, accrued interest, and visualize payment schedules with our comprehensive calculator
Please enter any four values into the fields below to calculate the remaining value of a bond. This calculator is for bonds issued/traded at the coupon date.
The par/nominal value of the bond
The annual interest rate paid on the bond’s face value
Time until the bond matures (in years)
The total return anticipated if held until maturity
How often interest payments are made
Results
| Bond Price | $0.00 |
| Total Interest | $0.00 |
| Number of Payments | 0 |
| Payment per Period | $0.00 |
Payment Breakdown
Use this calculator to value the price of bonds not traded at the coupon date. It provides the dirty price, clean price, accrued interest, and the days since the last coupon payment.
Method used to count days for accrued interest
Results
| Dirty Price | $0.00 |
| Clean Price | $0.00 |
| Accrued Interest | $0.00 |
| Interest Accrued Days | 0 |
| Last Coupon Date | – |
| Next Coupon Date | – |
Cash Flow Analysis
Amortization Schedule
| Period | Payment Date | Payment | Principal | Interest | Remaining Balance |
|---|---|---|---|---|---|
| Calculate a bond to view the amortization schedule | |||||
What is a Bond?
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically a corporation or government entity). It serves as a means for organizations or governments to raise funds by borrowing from investors. A bond specifies the terms of the loan and the payments to be made to the bondholder.
Bonds come in various types to cater to the diverse needs of both investors and issuers. Each type comes with its own unique characteristics, risks, and benefits. The most common types include government bonds, municipal bonds, corporate bonds, and high-yield (junk) bonds, among others.
Relative to stocks, bonds are considered a lower-risk investment, making them a popular choice among investors seeking a stable income stream while preserving capital. However, the risk and return on bonds can vary widely, depending on the creditworthiness of the issuer and the bond’s duration.
Bond Structure
The structure of a bond refers to its various components and characteristics, which dictate how it functions as a financial instrument. Here’s a breakdown of the key elements in the structure of a bond:
- Face value—The face value, or par value, is the amount the bond issuer agrees to repay the bondholder at the bond’s maturity. This amount also serves as the basis for calculating interest/coupon payments.
- Maturity date—The maturity date is the point when the bond’s principal is due for repayment to the bondholder. Bonds can have short, medium, or long-term maturities spanning from less than a year to over 30 years.
- Coupon rate—The coupon rate is the interest rate the bond issuer commits to paying on the bond’s face value. Interest is typically paid annually or semi-annually.
- Coupon payment frequency—This refers to how often interest payments are made to bondholders. Common frequencies include annual, semi-annual, quarterly, and monthly schedules.
- Yield—The yield is a measure of the return an investor anticipates earning if the bond is held to maturity. Expressed as an annual percentage, the yield is affected by the bond’s purchase price, face value, coupon rate, and the time until maturity.
- Price—The price of a bond is the amount it can be bought or sold for in the financial markets. In essence, a bond’s price reflects the present value of its future cash flows.
How to Calculate the Bond Price
Calculating the bond price involves discounting the future cash flows, which include interest payments and the principal repayment, to their present value using the required yield or discount rate. The bond price is the sum of the present values of all these cash flows. The basic formula for calculating the price of a bond is as follows:
Bond Price = Σ [ C/(1+r)^t ] + [F/(1+r)^n]
where:
C = the coupon payment per period,
N = number of periods until maturity,
r = the discount rate or yield per period,
F = the face value of the bond.
Example:
Let’s say we have a bond with a face value of $1,000, a coupon rate of 5%, semi-annual payments, a maturity of 10 years, and we require a yield of 6%.
Coupon payment per period (C) = 5% of $1,000 / 2 = $25
Number of periods (N) = 10 years × 2 = 20 periods
Discount rate per period (r) = 6% / 2 = 3% or 0.03
The bond price is calculated by discounting each semi-annual payment and the face value at maturity back to their present value, using a 3% per period rate. For this case, the calculated bond price is $925.61.
Clean Price and Dirty Price
When calculating the price or present value of a bond, it is often assumed that the bond trades or is issued on the coupon date. However, in reality, bonds are mostly traded outside of the coupon dates. In the bond market, the terms ‘clean price’ and ‘dirty price’ are used to distinguish between two ways of quoting the price of a bond outside the coupon date.
Accrued Interest
Accrued interest of a bond is the interest that has accumulated on the bond since the last interest payment date but has not yet been paid to the bondholder. The accrued interest can be calculated using the formula:
Accrued Interest = Coupon Rate × Face Value × (Days since last coupon / Days in coupon period)
Clean Price
The clean price of a bond is the price that excludes any accrued interest since the last coupon payment. When bonds are quoted in financial markets and to the public, the clean price is typically used. This price reflects the market value of the bond itself, without considering any accrued interest.
Dirty Price (Invoice Price)
The dirty price of a bond, also known as the invoice price, is the price that includes the accrued interest on top of the clean price. The dirty price is the actual amount paid by a buyer to the seller of the bond.
Dirty Price = Clean Price + Accrued Interest
Day-Count Conventions
Day-count conventions in the bond market are rules that determine how days are counted for the calculation of interest that accrues over time on bonds. The main day-count conventions include:
- 30/360 (bond basis): This convention assumes that each month has 30 days and a year has 360 days. Often used for corporate, agency, and municipal bonds.
- Actual/360 (A/360): The actual number of days in the accrual period is used, but the year is assumed to have 360 days. Common for money market instruments.
- Actual/365 (A/365): Uses the actual number of days in the accrual period but assumes a fixed year length of 365 days. Used for some government bonds outside the U.S.
- Actual/Actual (A/A): Takes into account the actual number of days in the accrual period and the actual number of days in the year. Used primarily for government bonds, including U.S. Treasury securities.