US Bonds Calculator: Price, Yield & More

This calculator works out the clean price of a US Treasury bond (or any fixed-rate bond) from its face value, coupon rate, years to maturity, and current market yield. You enter those four numbers and get back the price you would pay per $100 of face value, plus the current yield and the dollar price for a $1,000 bond. The math uses the standard present-value formula that prices every coupon bond in the market.

Formula

The price of a fixed-rate bond is the sum of two present values: the present value of all future coupon payments and the present value of the principal repaid at maturity. For a bond paying semiannual coupons, the formula is:

P = (C/2) × [1 − (1 + r/2)^(−2n)] / (r/2) + F / (1 + r/2)^(2n)

• P = clean price per $100 of face value (in dollars)
• C = annual coupon rate (as a decimal, e.g., 0.035 for 3.5%)
• r = annual yield to maturity (as a decimal, e.g., 0.042 for 4.2%)
• n = years to maturity
• F = face value (usually $100 per bond, but the calculator also accepts $1,000 or any other amount)

The coupon payment each half-year is C/2 per $100 of face value. The yield is also halved because it is an annual rate compounded semiannually, which is the convention for US Treasuries.

Worked Example

Using the defaults from the calculator: face value = $1,000, coupon rate = 3.5%, yield to maturity = 4.2%, years to maturity = 10.

1. Coupon per half-year = 3.5% / 2 = 1.75% → $1.75 per $100 face.
2. Number of periods = 2 × 10 = 20.
3. Yield per half-year = 4.2% / 2 = 2.1% = 0.021.
4. Present value of coupons = 1.75 × [1 − (1.021)^(−20)] / 0.021 = 1.75 × 16.1142 = 28.20 (rounded).
5. Present value of principal = 100 / (1.021)^20 = 100 / 1.5163 = 65.95.
6. Clean price per $100 = 28.20 + 65.95 = 94.15.
7. Dollar price for $1,000 face = 94.15 × (1000/100) = $941.50.
8. Current yield = (3.5 / 94.15) × 100 = 3.72%.

The calculator shows the same results: price = 94.15, current yield = 3.72%, dollar price = $941.50.

How to Read the Result

The clean price is what you see quoted in financial news. It does not include accrued interest, which is the interest that has built up since the last coupon payment. When you actually buy a bond between coupon dates, you pay the clean price plus accrued interest (the dirty price). For a newly issued bond or one bought exactly on a coupon date, the clean price equals the dirty price.

A price below $100 means the bond trades at a discount; above $100 means a premium. This happens automatically when the yield to maturity is higher or lower than the coupon rate. If the yield equals the coupon rate, the price is exactly $100 (par).

The current yield is simply the annual coupon divided by the price. It is a quick income measure but ignores capital gains or losses at maturity. The yield to maturity (YTM) is the more complete measure because it includes both coupon income and the difference between purchase price and face value.

Choosing the Right Yield to Maturity

The calculator requires you to input a yield to maturity. Where do you get it? For US Treasuries, you can look up the current yield on the US Department of the Treasury’s website, which publishes daily yield curves for maturities from 1 month to 30 years. For a specific bond, you can find its YTM on financial data sites like Bloomberg or Yahoo Finance, or from your broker’s bond desk.

If you are pricing a bond that is not a Treasury (e.g., a corporate or municipal bond), you need the yield for a bond with similar credit risk and maturity. The calculator works for any fixed-rate bond, but the yield you input must reflect the market’s required return for that specific issuer and term.

Common Mistakes and Misconceptions

• Mixing up coupon rate and yield. The coupon rate is fixed at issuance; the yield changes with market prices. The calculator uses the coupon rate to compute cash flows and the yield to discount them.
• Forgetting semiannual compounding. US Treasuries pay coupons every six months. Using annual compounding will give a slightly different price. The calculator uses the correct semiannual convention.
• Ignoring accrued interest. The price shown is clean. If you buy between coupon dates, you will pay extra for the interest that has accrued to the seller. The calculator does not compute that because it depends on the exact settlement date.
• Assuming price equals value. The calculated price is the theoretical fair value based on the yield you input. The actual market price may differ slightly due to liquidity, supply/demand, or bid-ask spreads.
• Using the wrong face value. US Treasury bonds typically have a $1,000 face value, but some older issues or other bonds may differ. The calculator lets you adjust it.

Limits of the Formula

The formula assumes a fixed coupon rate, a constant yield to maturity, and that all coupons are reinvested at that same yield. In reality, yields change daily, so the actual return you earn may differ. The formula also ignores taxes, transaction costs, and the possibility of early redemption (callable bonds). For callable bonds, the price may be lower because the issuer can redeem early if rates fall. The calculator is for non-callable, fixed-rate bonds only.

For zero-coupon bonds (like Treasury STRIPS), the coupon rate is 0%, and the formula simplifies to P = F / (1 + r/2)^(2n). You can still use this calculator by entering 0 for the coupon rate.

Alternatives and Related Tools

If you need to find the yield given a price, you can use a bond yield calculator, which solves the same equation for the yield. Many financial websites offer such tools. For more complex bonds (floating rate, inflation-indexed like TIPS, or callable), you need specialized calculators or a financial advisor. The US Treasury’s own website provides official yield data and auction results, which are useful for getting current market yields.

Frequently Asked Questions

What is the difference between clean price and dirty price?

Clean price is the bond’s price excluding accrued interest. Dirty price is what you actually pay: clean price plus interest accrued since the last coupon payment. For example, if a bond pays a $2 coupon every six months and you buy three months after the last payment, you pay the clean price plus $1 in accrued interest. The calculator gives the clean price.

Why does the price go down when yields go up?

Because the coupon payments are fixed. If market yields rise, new bonds pay higher coupons, making existing bonds less attractive. To compete, the existing bond’s price must fall so its yield rises to match the market. This inverse relationship is the core of bond pricing.

How do I find the yield to maturity for a specific Treasury bond?

Look up the bond’s CUSIP (a unique identifier) on the Treasury’s website or a financial data provider. The YTM is usually listed alongside the price and coupon. Alternatively, you can use the Treasury’s daily yield curve for a benchmark maturity as an approximation.

Does the calculator work for TIPS (inflation-protected securities)?

No. TIPS have a principal that adjusts with inflation, and the coupon is applied to the adjusted principal. The standard fixed-rate formula does not account for that. Use a TIPS-specific calculator or consult the Treasury’s TIPS data.

What is accrued interest and how do I calculate it?

Accrued interest is the portion of the next coupon payment that has accumulated since the last coupon date. For a semiannual bond, it equals (days since last coupon / days in coupon period) × (annual coupon / 2). For example, if 90 days have passed in a 182-day period and the coupon is $2, accrued interest is (90/182) × $2 = $0.99.

Why is the current yield different from the yield to maturity?

Current yield only measures annual coupon income relative to price. Yield to maturity includes that income plus the gain or loss you realize if you hold the bond to maturity. For a bond bought at a discount, YTM is higher than current yield because you also earn the price appreciation.

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in fv | Face value | $ | 1000 | 0
in cr | Coupon rate | % | 3.5 | 0
in ytm | Yield to maturity | % | 4.2 | 0
in years | Years to maturity | years | 10 | 0
out price | Clean price per $100 | $ | (cr/2 * (1 - (1 + ytm/200)^(-2*years)) / (ytm/200) + 100 / (1 + ytm/200)^(2*years)) | 2
out cur_yield | Current yield | % | (cr / price) * 100 | 2
out dollar_price | Dollar price for face value | $ | price * (fv / 100) | 2