Bond yield calculator
This bond yield calculator works out the yield to maturity from price, coupon and remaining term – or the fair price for a yield you want. A bond with a 5% coupon and 10 years to run is worth 1,081.11 per 1,000 face value at a 4% yield.
Source: Wikipedia – Bond valuation (price as present value of coupons and face value, clean and dirty price). Updated: .
How it is calculated
How to calculate a bond yield
A bond’s price is the sum of all future payments discounted at the yield: price = Σ coupon ÷ (1 + r)t + face value ÷ (1 + r)n. The yield to maturity is the rate r at which this value equals today’s price. The calculator finds r by bisection.
Example
Face value 1,000, coupon 5%, 10 years, yield 4%: the ten coupons of 50 have a present value of 405.54, the repayment of 1,000 has 675.56 – together 1,081.11. As a check, a price of 950 gives a yield of about 5.7%.
Price, yield and duration
- Price and yield move in opposite directions: when the yield rises, the price falls.
- Current yield is coupon ÷ price and ignores any gain or loss until repayment.
- Macaulay duration is the average time your money is tied up, in years; modified duration approximates how many percent the price moves for a 1 percentage point change in yield.
Honest limits
The calculator assumes the purchase date coincides with a coupon date and ignores accrued interest, taxes and fees; the real purchase price includes accrued interest. The yield is a nominal annual rate for the chosen payment frequency; with annual payments it equals the effective yield. Floating-rate bonds, callable bonds and default risk are not modelled. This is not investment advice.
Frequently asked questions
How do I calculate the yield of a bond?
The yield to maturity is the rate at which the present value of all coupons and the repayment equals the price. The calculator finds it automatically.
What is the formula for bond yield?
Price = Σ coupon ÷ (1 + r)^t + face value ÷ (1 + r)^n, solved numerically for r. The simple approximation is coupon ÷ price (current yield).
What does trading above or below par mean?
Par is face value (100%). Below par the yield is higher than the coupon; above par it is lower.
What does duration tell me?
It measures the average time your capital is tied up and the interest rate risk: the higher the modified duration, the more the price moves when rates change.
Is accrued interest included?
No, the price is a clean price. When you buy, you also pay the interest accrued since the last coupon.
Sources and legal basis
- Wikipedia – Bond valuation (price as present value of coupons and face value, clean and dirty price)
- Wikipedia – Yield to maturity
- Wikipedia – Bond duration (Macaulay and modified duration)
As of:
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