Yield to Maturity Calculator

Clean price per 100 = Σ (Coupon per period ÷ (1 + y ÷ m)^t) + 100 ÷ (1 + y ÷ m)^(m × n)

Clean price per 100

What you pay for each 100 of face value, with accrued interest left out; the yield is the rate that discounts every remaining payment down to exactly this number

Coupon rate

The coupon as a percentage of face value per year, paid in m equal instalments; zero is allowed and describes a bond that pays nothing until maturity

m

How many coupon payments arrive each year (annually, twice a year, quarterly or monthly); the same bond quoted at two frequencies is two different yields

n

Years left until the face value is repaid, as a whole number, so the number of remaining payments is m × n

y

The yield to maturity: the nominal annual rate, compounded m times a year, that solves the equation — the convention bond desks quote

Effective annual yield

The same rate restated as one yearly growth factor, (1 + y ÷ m)^m − 1; it is always higher than y whenever m is greater than one, and the gap is the compounding

Current yield

One year of coupons divided by the clean price, ignoring the gain or loss as the bond returns to face value — which is exactly why it disagrees with the yield to maturity on any bond not priced at par

Use it to compare bonds of different coupons and different maturities on one scale, which is what the quoted yield is for: a 2 percent coupon bond at 92 and an 8 percent coupon bond at par can be ranked by this number when they cannot be ranked by their coupons. Use it to check a price someone quoted you, or to see what a price implies about the rate the market is demanding. It is the wrong tool in three places. It assumes you hold to maturity and that every coupon is reinvested at the same rate, which is a promise no market makes — a bond held through falling rates will earn less than its yield to maturity said. It is a nominal rate compounded at the coupon frequency, so a twice-a-year bond and a monthly bond quoted at the same yield are not paying the same amount over a year; that is what the effective annual yield beside it is for. And it says nothing about credit: a yield well above the government curve on the same maturity is the market pricing a real chance of not being repaid.

1. A 4% ten-year bond at 92.205 per 100

   1. Coupons per year: 4.00 per 100 of face value, paid as 2.00 twice a year, so 20 payments of 2.00
   2. Find the rate that discounts 20 payments of 2.00 plus 100 at the end to 92.205: 2.5% per half year
   3. Quote it the way bond desks do, doubling the half-year rate: 5.000% a year
   4. Restate it as one yearly factor: 1.025 × 1.025 − 1 = 5.0626% effective
   5. Current yield, which ignores the pull to par: 4.00 ÷ 92.205 = 4.34%

   This is the page's default, and the last two lines are the point of it. The quoted 5.000% and the 5.0626% are the same rate written under two conventions, and the second one is what the money actually does over a year — 0.0626 is not rounding, it is the half-year compounding. The current yield of 4.34% is the smallest of the three and the one most often quoted in a newspaper, because it is the only one you can work out in your head; it is also the only one that does not notice you are buying the bond 7.795 below face value and will be repaid at 100.

2. A zero-coupon bond at 61.027 pays 5% and a 0% current yield

   1. The coupon rate is zero, so every coupon in the equation is 0.00 and only the 100 at maturity is left
   2. 100 ÷ 1.025^20 = 100 ÷ 1.638616 = 61.027
   3. Quote it the way bond desks do: 2.5% per half year, doubled to 5.000% a year
   4. Restate it as one yearly factor: 1.025 × 1.025 − 1 = 5.0625% effective
   5. Current yield: 0.00 ÷ 61.027 = 0.00%

   A zero-coupon bond is where the two conventions come apart most cleanly, because there is no coupon to confuse the arithmetic: the entire return is the 38.973 between the price and the face value, and it arrives all at once. The quoted yield is 5.000% and the effective annual yield is 5.0625%, and the difference between them is the whole of the compounding. The current yield is exactly zero — a reader who screens bonds by current yield will never see this one, which is the clearest argument for not screening by it.

3. A price with one decimal: 95.5 gives 4.566%

   1. Coupons: 20 payments of 2.00, with 100 repaid at the end
   2. Solve for the half-year rate that discounts that stream to 95.5: 2.2831% per half year
   3. Double it for the quoted yield, printed to three decimals: 4.566% a year
   4. Effective annual yield: 1.022831 × 1.022831 − 1 = 4.6177%
   5. Current yield: 4.00 ÷ 95.5 = 4.19%

   Prices in the market are quoted to a fraction of a point, not to whole numbers, and the yield that comes back is almost never a round figure — so this page prints three decimals for the quoted yield and four for the effective one. The three figures still hold their order: the effective annual yield is above the quoted yield, and the current yield is below both, because at 95.5 the bond is still bought at a discount and the 4.5 of pull to par belongs to whoever holds it to the end.

Three things this number is not. It is not a promise: the yield to maturity assumes every coupon is reinvested at the same rate until maturity, and if rates fall in the meantime you will earn less than it said — that gap is called reinvestment risk and no yield quote can price it away. It is a nominal rate compounded at the coupon frequency, so it is not comparable across bonds that pay at different frequencies until you look at the effective annual yield beside it. And it uses the clean price, with accrued interest left out, which is right for pricing a bond between coupon dates but means the price here is not the amount of cash you hand over. The current yield beside it is a simpler measure with a specific blind spot: because it ignores the difference between the price and the face value, it understates the return on a discounted bond and overstates it on one bought at a premium, and on a zero-coupon bond it is zero no matter how much the bond earns. Finally, nothing here knows about credit risk, taxes or call provisions; a bond that can be redeemed early may never reach the maturity this page assumes.

How do I calculate yield to maturity?

It is the rate that discounts every remaining payment — each coupon and the face value at the end — down to the price you are paying. There is no way to rearrange the formula to get it directly, so it is found by searching: try a rate, price the bond at it, and narrow the range until the price matches. On a 4% ten-year bond at 92.205 per 100, paid twice a year, the answer is 2.5% per half year, quoted as 5.000% a year.

Why is the clean price per 100 of face value rather than a dollar amount?

Because the face value cancels out of the equation, so quoting per 100 makes two different bonds comparable at a glance and removes one field that could only ever be filled in wrongly. A bond at 92.205 is at 92.205% of face value whether the face value is 100 or 1,000,000. Entering the dollar price instead — 922.05 for the same bond — does not produce an error message; it produces a yield below zero, because the arithmetic obliges you to hand back the 100 that the equation assumes.

What is the difference between the yield to maturity and the effective annual yield?

Two conventions for writing the same rate. The quoted yield to maturity is nominal: it is the rate per period multiplied by the number of periods, so 2.5% twice a year is written 5.000%. The effective annual yield restates it as the growth factor over a full year, 1.025 × 1.025 − 1 = 5.0626%, which is what the money actually does. They are equal only when the coupon is paid once a year. On quarterly payments the same 5.000% quoted is 5.0946% effective, and on monthly payments 5.1162% — the more often interest compounds, the wider that gap.

Why is the current yield different from the yield to maturity?

Because the current yield only counts the coupons. It is one year of coupons divided by the price, and it says nothing about the fact that a bond bought below face value will be repaid at face value, which is a real part of the return. On the default example the coupon is 4.00 against a price of 92.205, so the current yield is 4.34%, while the yield to maturity is 5.000% — the missing 0.66 of a point is the 7.795 of pull to par, spread over ten years. On a bond priced at exactly 100 the two agree, and on a zero-coupon bond the current yield is zero no matter what the bond earns.

Does the coupon frequency change the answer?

It changes the quoted number even when the bond is worth exactly the same. Ten years of 4% coupons are 40.00 per 100 in total whichever way they are paid, but the discounting differs: the same bond priced to yield 5% a year costs 92.278 with annual payments, 92.168 quarterly and 92.143 monthly. Two reasons. The nominal quote is per-period times periods, so the same effective return is written as a bigger nominal number the more often it compounds. And payments that arrive sooner are worth more, so a monthly bond is worth slightly more than an annual one at the same quoted rate.

What does a yield to maturity above the coupon rate mean?

That the bond is priced below face value, so part of your return is the gain you make when it is repaid at 100. On the default example the coupon is 4% and the yield is 5.000% because the price is 92.205. The reverse holds too: a bond priced above face value yields less than its coupon, because you take a loss as it comes back to par. The extreme case is the reference table's first row, where a price of 140 per 100 is exactly the sum of all the remaining payments with no discounting at all — the yield is 0%, and any price above it has no non-negative answer.

• Understanding Pricing and Interest Rates — why a note or bond sells at a discount or a premium, and what the quoted yield means — U.S. Department of the Treasury, Bureau of the Fiscal Service (TreasuryDirect), United States
• Yield — Investor.gov glossary, for the rate a bond's payments imply at a given price — U.S. Securities and Exchange Commission, Investor.gov (United States)
• Bonds — Investor.gov glossary, for the coupon, the face value and the maturity date that the equation is built out of — U.S. Securities and Exchange Commission, Investor.gov (United States)
• 31 CFR Part 356, Appendix B — Formulas and Tables: the present value formula the Treasury uses to price its own notes and bonds from a yield — U.S. Department of the Treasury rule, via the Electronic Code of Federal Regulations (United States)