Bond price calculator
Enter the face value, coupon rate, yield to maturity and the years left. The calculator discounts every remaining coupon and the repayment at the yield and shows the price you would see quoted (clean), the price you would pay (dirty), and the bond's duration.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the face (par) value, the annual coupon rate and the yield to maturity.
- Enter the years left to maturity. A whole number of coupon periods means today is a coupon date; a fraction means part of a period has passed.
- Choose how often the coupon is paid.
How it works
With f payments a year, the coupon per period is C = face × coupon ÷ f and the yield per period is i = yield ÷ f. The number of periods left is n = years × f; the next coupon is w = n − (N − 1) periods away, where N is n rounded up.
- Dirty price = Σ C ÷ (1 + i)^(k − 1 + w) for k = 1…N, plus face ÷ (1 + i)^(N − 1 + w).
- Accrued interest = C × (1 − w); clean price = dirty − accrued.
- Current yield = annual coupon ÷ clean price.
- Macaulay duration = Σ (time in years × present value) ÷ dirty price; modified = Macaulay ÷ (1 + i).
Worked example
A 1,000 bond with a 5% semiannual coupon, 10 years left, priced at a 6% yield: C = 25, i = 3%, N = 20.
- Coupons: 25 × (1 − 1.03^−20) ÷ 0.03 = 25 × 14.8775 = 371.94.
- Face: 1,000 ÷ 1.03^20 = 553.68.
- Price = 925.61, a discount of 74.39, because the yield is above the coupon. Current yield 50 ÷ 925.61 = 5.402%.
Tips
- Price and yield move in opposite directions. Longer bonds and lower coupons mean a larger duration and bigger price swings.
- Use the bond yield calculator for the reverse: the yield from a price.
- For a zero-coupon bond enter a coupon of 0; its Macaulay duration equals its maturity.
Frequently asked questions
How is a bond's price calculated?
Each remaining coupon and the face value at maturity is discounted at the yield per period (annual yield ÷ payments a year), and the present values are added up. That sum is the dirty price; subtracting accrued interest gives the clean price.
What is the difference between clean and dirty price?
Between coupon dates the seller has earned part of the next coupon. The dirty price includes that accrued interest and is what the buyer pays; the clean price excludes it and is what is usually quoted.
Why is the price below face value?
When the yield is above the coupon rate, the bond pays less than the market wants, so it trades at a discount. When the yield is below the coupon, it trades at a premium. When they are equal, the price on a coupon date is the face value.
What do Macaulay and modified duration mean?
Macaulay duration is the average time to the bond's cash flows in years, weighted by their present values. Modified duration (Macaulay ÷ (1 + yield per period)) estimates the percent change in price for a 1-point change in yield.
Which day count does it use?
It works in fractions of a coupon period taken from the years you enter, not an exact day count such as 30/360 or actual/actual. Prices from a broker can differ by a few cents for that reason.