Bond Calculator

Bond price from yield (or yield from price), current yield, and duration.

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Educational estimate only — not investment, lending, or financial advice. Confirm figures with statements or a qualified professional before you act.

About this tool

Enter a face value, coupon rate, coupon frequency and years to maturity. Then either give a yield to get the price, or give a price to get the yield. Current yield and duration are shown alongside.

How to use

1
Step 1
Choose to find the price from a yield, or the yield from a price.
2
Step 2
Enter face value, coupon rate, coupons per year and years to maturity.
3
Step 3
Enter the yield, or the market price, depending on the mode.
4
Step 4
Press Calculate.

How it works

A bond's price is the present value of its coupons plus the face value, discounted at the yield. When the yield is above the coupon rate the bond trades below par, and vice versa. Macaulay duration is the weighted-average time to receive the cash flows; modified duration estimates how much the price changes for a small change in yield. Valuation is assumed to be on a coupon date, with a whole number of coupon periods to maturity.

price = Σ coupon ÷ (1 + y)^t + face ÷ (1 + y)^n      y = yield ÷ coupons per year

Worked example

A 10-year 5% bond at a 6% yield

Input
Face 1,000; coupon 5%; 2 a year; 10 years; yield 6%
Output
Price $925.61; current yield 5.402%; Macaulay duration 7.895 years; modified duration 7.665 years
Walkthrough
Each coupon is 25. Discounting 20 coupons and the 1,000 face at 3% per half year gives 925.61. Going the other way, a price of 950 gives a yield to maturity of 5.6617%. At a 5% yield, the same bond prices at exactly 1,000.

Limitations

  • Valuation date must be a coupon date; years to maturity times coupons per year must be a whole number.
  • Yield is compounded at the coupon frequency.
  • No accrued interest, taxes, call features or credit risk. For accrued interest use the Bond Accrued Interest Calculator.

Questions

How do I price a bond?
Discount each coupon and the face value at the yield per period. For a 10-year 5% semi-annual bond at 6%, the price is $925.61.
Why is the price below face value?
Because the coupon rate (5%) is lower than the yield (6%) that investors require, so the bond sells at a discount.
What is yield to maturity?
The annual rate that makes the present value of all remaining payments equal today's price. At 950 it is 5.6617%.
What does duration tell me?
How sensitive the price is to yield changes. Modified duration of 7.665 means roughly a 7.7% price fall for a 1 percentage point rise in yield.

Features

  • Price from yield or yield from price
  • Current yield
  • Macaulay and modified duration
  • Runs in your browser

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Compound interest introduction

    Khan Academy

    Core compounding behind TVM and ICONV tools.

    Watch on YouTube

  • Introduction to bonds

    Khan Academy

    Coupon and yield basics for bond calculators.

    Watch on YouTube

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