Bond Calculator: Price, Yield and Accrued Interest

Bond Calculator Inputs: What Each Field Means

Every tool of this kind asks for the same building blocks, because a bond is simply a loan with a fixed schedule of payments. Knowing what each field represents makes the output far easier to trust. Try the cash back or low interest calculator to run your own numbers — everything is calculated in your browser and nothing you enter is stored or sent anywhere.

• Face value (also called par value): the principal the issuer repays at maturity, and the base for every coupon payment.
• Coupon rate: the annual percentage the borrower pays on the face value, not on what you paid.
• Yield: the return the market currently demands, used as the discount rate in the price formula.
• Time to maturity: how many years remain before the principal comes back, which sets the number of payments.
• Coupon payment frequency: annual or semi-annual payments, which changes both the payment size and the discounting period.

Face Value and Par Value

The face value of most corporate and government issues is $1,000, though other denominations exist. Price is often quoted per $100 of par value, so a quote of 92.84 means $928.40 for a $1,000 note. The principal you receive back never changes, which is why a lower purchase price lifts an investor's total return.

Coupon Rate and Coupon Payment Frequency

A 4.35% coupon on $1,000 produces $43.50 of interest each year. Paid semi-annually, that becomes two payments of $21.75. The calculator needs the frequency because it divides both the coupon and the yield by the number of periods per year.

Time to Maturity and Maturity Date

Time to maturity runs from the settlement day to the maturity date. Longer terms mean more coupon payments and greater sensitivity to rate changes, a point that matters in the duration discussion further down.

How a Bond Pricing Calculator Works

A bond pricing calculator applies one idea: the price equals the present value of everything the issue will pay you. Each coupon and the final principal are discounted at the market yield for the number of periods until it is received. The cash and equities questionnaire uses the same plain-English approach, so you can compare results side by side.

Here C is the coupon payment per period, r is the yield per period, N is the number of periods and F is the face value. The first term is the stream of coupon payments and the second is the principal, so the two parts together are the full set of cash flows.

Bond Structure and Cash Flows

The bond structure is what makes this formula possible: a fixed-rate coupon schedule, a known maturity and a stated principal. Features such as call and put options, covenants, credit rating and marketability do not appear in the equation, yet they change what the market will accept as a yield. Pricing a callable or floating issue needs a more advanced model than a simple pricing calculator.

Present Value of Each Coupon Payment

Every bondholder collects the same coupon, but one due in three years is worth less than one due next year, because its present value is discounted three times. Adding up all fourteen discounted payments in the example below gives $249.07, while the discounted principal contributes the larger share.

Worked Example: Pricing a Seven-Year Bond

Suppose you are looking at a seven-year note with a $1,000 face value, a 4.35% annual coupon paid semi-annually, while the market yield sits at 5.6%. Each step uses the formula above:

1. Coupon payment per period: 4.35% × $1,000 ÷ 2 = $21.75.
2. Number of periods: 7 years × 2 = 14.
3. Yield per period: 5.6% ÷ 2 = 2.8%.
4. Discount all 14 payments and the principal at 2.8% and add them together.

Reading the Result: Discount, Par or Premium

The result of $928.43 sits $71.57 below face value because the 4.35% coupon is lower than the 5.6% market yield. A buyer holding to maturity collects $304.50 in total interest payments plus the $1,000 principal. When the coupon matches the yield, the price equals par, and when the coupon is higher, the price rises to a premium. The current yield here is 4.69%, which is the annual coupon of $43.50 divided by the $928.43 market price.

Checking a Fixed-Income Offer Before Placing an Order

Marguerite is rebuilding the fixed-income part of her savings portfolio, and her broker lists a corporate issue with a $1,000 face value, a 3.875% coupon paid semi-annually and 9 years left. The screen shows an ask yield of 5.12%, and her investment policy statement sets a 5.00% minimum yield for anything she buys, so she wants the dollar price before she commits.

She enters the face value of 1,000, a coupon rate of 3.875, a yield of 5.12, 9 years to maturity and semi-annual payments. The coupon payment comes out to $19.375 per period, there are 18 periods, and the discount rate is 2.56% per period. The calculator returns a price of $911.11, a discount of $88.89 to par, with a current yield of 4.25% (the $38.75 annual coupon over $911.11).

The broker's quote of 91.11 matches, so the screen is consistent with the formula. Marguerite's real decision is about the 5.00% floor: a 5.12% yield clears it by 12 basis points, but the margin is thin. She reruns the calculator with only the yield changed to 5.40%, the level where she would be comfortable if the issue slips further, and sees the price drop to $892.42. For a ten-bond lot, that means $9,111.10 at today's quote against $8,924.20 at the lower price. She places a limit order at 91.11 instead of a market order, and keeps the $186.90 difference in mind as the cushion she will not chase.

Clean Price, Dirty Price and Accrued Interest

The example above assumes you buy exactly on a coupon date. In practice most trades happen mid-period, so the price you see quoted and the cash you actually pay differ by the accrued interest.

Clean Price

The clean price strips out accrued interest, so it moves only when yields or credit conditions move. Dealers quote it so different issues can be compared on equal terms.

Dirty Price (Invoice Price)

The dirty price, also called the invoice price, is what the buyer really pays: dirty price = clean price + accrued interest. With 74 days since the last coupon payment under a 30/360 count, accrued interest is $1,000 × 4.35% × 74 ÷ 360 = $8.94, so a clean price of $928.43 becomes a dirty price of $937.37. The days since the last coupon payment is what tells the seller how much interest was earned before the sale.

Day-Count Conventions Behind the Bond Price

Counting interest accrued days is not universal. The day-count convention depends on the market, and the matching dropdown in the calculator changes the accrued interest and the dirty price slightly.

• 30/360 (bond basis): every month has 30 days and a year has 360, common for corporate and municipal bonds in the United States.
• Actual/360: real days elapsed over a 360-day year, typical of money market paper, commercial paper and certificates of deposit.
• Actual/365: real days over a 365-day year, used by some government bonds outside the US.
• Actual/actual: real days over the real year length, the standard for Treasury securities.

The difference between conventions is usually small, at most a few days of accrued interest, but a good calculator lets you choose so the settlement figure matches your broker's statement.

How Savings Bonds Differ from Market Bonds

Savings bonds issued by the Treasury are not traded, so their value follows a published schedule rather than a market yield. You cannot discount them with the formula above; instead you look up the issue date and denomination in a savings bond calculator on the Treasury's site. By contrast, a marketable issue changes price every trading day. Use that tool for savings bonds, and return to the formula above for anything that trades.

Choosing the Yield to Enter for Each Bond Type

The yield you enter reflects who issued the security and how financial markets judge that issuer. Government bonds, municipal bonds and corporate bonds each carry a different premium for risk:

• Treasury bonds and other government bonds: the lowest credit risk, backed by the national budget.
• Municipal bonds: issued by states and cities, with tax advantages that shape the yield.
• Corporate bonds: higher yield for higher credit risk, down to high-yield junk bonds with weaker credit quality.
• Zero-coupon bonds: no coupon at all, so the whole return comes from buying below par and receiving the principal at maturity.

A higher-risk issuer must offer a higher yield, and entering it lowers the calculated price. Relative to stocks, bonds are lower risk and less volatile, a common stable income choice for retirees and conservative investors, but they still fall in value when interest rates rise.

Why Price and Yield Move in Opposite Directions

A yield calculator view of the same example shows the inverse relationship. Because the coupon is fixed, a rising yield can only be matched by a falling price.

This is why the interest rate environment, supply and demand and inflation all feed into what a seller can get. It also shows why a longer duration means a bigger price swing: more years of fixed payments are exposed to the same discount rate. The current yield and the yield to maturity are two different measures, and the second one is the figure that includes the discount you earn as the price pulls back to par.

Who Uses a Fixed-Income Calculator

An investor comparing a primary market purchase with a secondary market quote use it to check value before trading. Retirees mapping out retirement use it to confirm how much income an issue will pay, and savers deciding between certificates of deposit and a loan to a corporation run the same numbers to compare return and risk. This tool is built for a fixed-rate coupon bond, and a financial calculator of this kind will not account for credit quality or call features, so treat its output as the theoretical fair value rather than a guarantee. A yield to maturity assumes you reinvest each coupon at that same yield, the compound interest logic behind the price formula. For capital planning, remember that a bond held to maturity returns the principal regardless of what happened to the market in between.