Bond Yield Calculator
Find a bond's yield to maturity and current yield from its price, or the price for the yield you want, with yield to call, accrued interest, duration and every payment you'll get.
Paid twice a year. Change it in Advanced.
Yield to maturity, the return if you hold to the end.
Markets quote the clean price; you pay the dirty price.
Used with exact dates to work out accrued interest.
Cash flows and price–yield curve
How your bond yield is worked out
Yield to maturity is the one rate that makes every future payment, discounted back, add up to the price.
- 1
Coupon each period
$1,000.00 × 5%÷ 2 a year= $25.00
- 2
Current yield
$50.00 a year÷ $950.00= 5.26%
- 3
Balance the price
20 payments, worth$950.00 today at2.8308% a period
- 4
Yield to maturity
2.8308% × 2= 5.662% a year
Read more: the formula, a worked example, clean vs dirty price, duration and yield to call
A bond is a loan you make to a government or company. It pays a fixed coupon (interest) on a schedule and gives back the face value on the maturity date. Its price moves with market rates, so the return you actually earn depends on what you pay. Yield to maturity (YTM) is that return: the one yearly rate that makes the value today of every coupon plus the face value equal the price.
The formula
price = coupon ÷ (1 + r) + coupon ÷ (1 + r)^2 + … + (coupon + face) ÷ (1 + r)^n
coupon = face × coupon rate ÷ payments a year
r = rate per period; YTM = r × payments a year
current yield = yearly coupons ÷ clean price
quick YTM estimate = (yearly coupons + (face − price) ÷ years) ÷ ((face + price) ÷ 2)
There is no neat way to rearrange the price formula for r, so the calculator tries rates until the two sides match to many decimal places (the same thing Excel's YIELD and a financial calculator do).
Worked example
A bond with a $1,000 face value, a 5% coupon paid twice a year and 10 years left costs $950. Each coupon is $1,000 × 5% ÷ 2 = $25, and there are 20 of them. The current yield is $50 ÷ $950 = 5.26%.
At a rate of 2.8308% per half-year, (1.028308)20 = 1.7477. The 20 coupons are worth $25 × (1 − 1 ÷ 1.7477) ÷ 0.028308 = $377.82 today, and the $1,000 at the end is worth $1,000 ÷ 1.7477 = $572.18. Together that is $950.00, the price, so the yield to maturity is 2.8308% × 2 = 5.66% a year. Compounded, that is an effective (1.028308)2 − 1 = 5.74% a year. The quick estimate gives (50 + 50 ÷ 10) ÷ 975 = 5.64%, close but not exact.
Held to the end you get $500 of coupons plus $1,000, so $1,500 for $950: a profit of $550. The Macaulay duration is 7.93 years and the modified duration 7.71, so a 1% rise in yields would cut the price by about 7.7%. Repriced exactly, a yield of 6.66% gives $880.09 and 4.66% gives $1,026.80.
Price from a yield
Switch to "The price" in Advanced to go the other way. The same 5% bond priced to yield 6% is worth $25 × (1 − 1.03−20) ÷ 0.03 + $1,000 ÷ 1.0320 = $371.94 + $553.68 = $925.61.
Premium, discount and par
- Below face (discount): YTM is higher than the current yield, which is higher than the coupon rate, because you also gain the difference back at maturity.
- Above face (premium): the order flips; YTM is the lowest of the three.
- At face (par): all three are the same.
Clean price, dirty price and accrued interest
Between coupon dates the seller has earned part of the next coupon. That share is the accrued interest = coupon × days since the last coupon ÷ days in the period. Markets quote the clean price; you pay the dirty price = clean + accrued. With exact dates, pick the day count the bond uses: 30/360 counts every month as 30 days (common for US corporate and municipal bonds), Actual/Actual counts real days (US Treasuries, UK gilts and most government bonds), and Actual/365 or Actual/360 are used by some money-market and local bonds. If you enter years that aren't a whole number of coupon periods, the calculator treats you as part-way through a period in the same way.
Yield to call and yield to worst
A callable bond can be repaid early by the issuer at the call price. Yield to call works the yield as if that happens on the first call date. Yield to worst is the lower of yield to maturity and yield to call, the safer figure to plan with when a premium bond is likely to be called.
Duration and convexity
Macaulay duration is the average time, in years, until you receive the bond's money, weighted by the value of each payment. Modified duration = Macaulay ÷ (1 + rate per period) and tells you roughly how many percent the price moves for a 1% change in yield. Convexity corrects that straight-line guess for the curve. DV01 is the money change in price for a 0.01% (one basis point) move.
Zero-coupon bonds
A zero-coupon bond pays nothing until maturity, so price = face ÷ (1 + yield)years with yearly compounding. US Treasury strips are often quoted with twice-a-year compounding instead; the calculator shows that figure too.
For learning and comparison, not investment advice. Assumes every coupon is paid in full and on time, and coupons are reinvested at the same yield (the usual YTM assumption). Taxes, fees and broker commissions aren't included. A final coupon period is discounted with compounding; some systems use simple interest for the last period, which can change the yield slightly for bonds less than one period from maturity. The 30/360 count here is the US (NASD) version without the special February rule.
Common questions
What is yield to maturity?
Yield to maturity (YTM) is the yearly return you get if you buy a bond at today's price, hold it to the end and every coupon is paid and reinvested at the same yield. A $1,000 bond with a 5% coupon paid twice a year, 10 years left and a price of $950 has a YTM of 5.66% a year.
What is the difference between current yield and yield to maturity?
Current yield is just the yearly coupons ÷ the price: $50 ÷ $950 = 5.26% in the example. YTM also counts the gain or loss from getting the face value back at maturity, so it is higher than the current yield for a bond bought below face and lower for one bought above face.
Why do bond prices fall when yields rise?
A bond's price is the value today of all its future payments, worked out at the market yield. A higher yield makes those payments worth less today, so the price falls. Modified duration tells you roughly how much: in the example it is 7.71, so a 1% rise in yields cuts the price by about 7.7%.
What is the difference between a clean and dirty price?
Between coupon dates the seller has earned part of the next coupon, called accrued interest. Markets quote the clean price, without it; you pay the dirty price, which is the clean price plus accrued interest. The calculator works out accrued interest with the day count your bond uses.
What is yield to worst?
A callable bond can be repaid early by the issuer. Yield to call works out the yield as if that happens on the first call date, and yield to worst is the lower of yield to maturity and yield to call. It is the safer figure to plan with when a premium bond is likely to be called.
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