Bond Yield Calculator
A bond's current yield and yield to maturity from its price, coupon and years left, or the price that gives the yield you require.
Result…
How it's calculated
Price = C × (1 − (1 + r)^−n) ÷ r + F × (1 + r)^−n C = F × coupon rate ÷ k, r = yield ÷ k, n = years × k Yield to maturity: the yield that makes the price formula equal the market price Current yield = F × coupon rate ÷ price Effective yearly yield = (1 + r)^k − 1
A bond pays a fixed coupon each period and its face value at maturity. Its current yield compares a year's coupons with the price you pay, but ignores the gain or loss when the bond is repaid at face value. The yield to maturity (YTM) includes that: it is the single rate that discounts every coupon and the final repayment to exactly the price. A bond bought below face value (at a discount) has a YTM above its coupon rate; one bought above face value (at a premium) has a YTM below it. This page solves for the YTM by bisection, which always finds the one answer, or turns a required yield into a price. It values the bond on a coupon date, so accrued interest is out of scope. The chart shows how the price falls as yields rise.
Your numbers, step by step
About the Bond Yield calculator
This bond yield calculator finds the yield to maturity (YTM) and the current yield of a bond from its price, face value, coupon rate, how often the coupon is paid and the years left. Switch to “Price from yield” to turn it around and see what a bond is worth at the yield you require. Investors use it to compare bonds bought at a discount or a premium with each other and with savings rates, and students use it to check textbook problems. The yield to maturity has no direct formula, so the calculator narrows in on the one rate that makes the discounted coupons and the final repayment equal the price, and shows each step with your numbers. The chart draws the price against the yield, so you can see how prices fall as yields rise. It values the bond on a coupon date, so accrued interest is left out.
How to use it
- Choose “Yield from price” to find the yield, or “Price from yield” to value the bond at a yield you want.
- Enter the “Face value (par)” and either the “Price” or the “Required yield”.
- Enter the “Coupon rate” (0 for a zero-coupon bond) and how many “Coupons a year” it pays.
- Set the “Years to maturity” as a whole number of coupon periods, then read the yield to maturity, current yield and effective yearly yield.
Worked example
A bond with a face value of 1,000 and a 4.5% coupon paid twice a year has 8 years left and costs 960. Each coupon is 22.50, and 45 a year divided by 960 gives a current yield of 4.6875%. Solving for the rate that discounts the 16 coupons and the 1,000 repayment to 960 gives a yield to maturity of 5.1156% a year, or 5.1810% as an effective yearly rate. At a required yield of 5.5% the same bond would be worth 935.98, a discount of 64.02 to its face value.
Updated
Questions people ask
How do I calculate the yield to maturity of a bond?
Find the interest rate at which the present value of every remaining coupon plus the face value equals the price you pay. There is no direct formula, so it is solved by trial and narrowing, which this calculator does for you. It is the same idea as the IRR calculator applied to a bond.
What is the difference between current yield and yield to maturity?
Current yield is a year's coupons divided by the price. Yield to maturity also counts the gain or loss when the bond is repaid at face value, so it is higher than the current yield for a bond bought at a discount and lower for one bought at a premium.
Why do bond prices fall when yields rise?
A bond's coupons are fixed. When the yield buyers demand goes up, the same coupons are only worth a lower price, so the price falls until the bond offers the new yield. The chart on this page shows that curve for your bond.
Does the yield to maturity include accrued interest?
No. This page values the bond on a coupon date. Between coupon dates the buyer usually pays the seller accrued interest on top of the quoted clean price, and markets count days in different ways, so a broker's figure may differ slightly.
Is the yield to maturity what I will actually earn?
Only if you hold the bond to maturity, every payment is made in full and the coupons are reinvested at the same yield. Defaults, early calls, taxes and fees change the result. For decisions about your own money, talk to a qualified financial adviser.