Skip to content

Yield to maturity calculator

By Jude Wallis

Yield to maturity is the one discount rate that makes every remaining coupon plus the face value add up to today's price. A $1,000 bond paying a 5 percent coupon twice a year, with 10 years left and a price of $857.88, yields 7 percent.

Yield to maturity

7.00%

The one discount rate that prices every remaining coupon plus face at this price.

Yield to maturity
7.00%
Price
857.88
Face value
1000.00
$
$
%
yr

Put this on a class page: one iframe, free, for Google Sites, Canvas, WordPress or Notion.

On this page

The formula

P=∑t=1nC(1+y/m)t+F(1+y/m)nP=\sum_{t=1}^{n}\frac{C}{(1+y/m)^{t}}+\frac{F}{(1+y/m)^{n}}

PP is the price paid, CC is the coupon per period, FF is face value, mm is payments per year, nn is the periods left, and yy is the annual yield the solver searches for.

Why a discount price raises the yield

Buy at $857.88 and two separate things pay you. The coupon arrives twice a year and never changes, because it is fixed against face value. Then, at maturity, $1,000 arrives whatever you paid. That second piece is the reason a 5 percent coupon becomes a 7 percent yield: you collected the coupons and a gain on the way to face.

Run it the other way and the same logic holds. A price above face means you paid more than the $1,000 that comes back, so the pull to face works against you and the yield lands below the coupon rate. Price and yield move in opposite directions, always, and the size of the move grows with the years left. A yield is a rate you earn, not a rate the issuer set.

Coupon rate, current yield and YTM are three numbers

The coupon rate is set against face and never moves: 5 percent of face, paid as 1000×0.05/2=251000 \times 0.05 / 2 = 25 every six months. Current yield divides the annual coupon by what you actually paid, so 50/857.88=0.058350 / 857.88 = 0.0583, 5.83 percent. Yield to maturity is the only one of the three that also counts the $1,000 arriving at the end, which is why it reaches 7 percent.

On a bond bought at par all three collapse into the same figure, which is exactly why the difference is easy to miss. Current yield against YTM sets the two side by side, and the current yield calculator does the simpler half of the job.

The solve is a search, not a rearrangement

There is no algebra that isolates yy in the pricing equation once there is more than one coupon left. Every yield to maturity you have ever seen was found by trying a rate, pricing the bond at it, and moving. This calculator brackets the answer and halves the bracket until the price it produces matches the price you typed.

That is also why yield quotes can differ by a basis point between systems: day count, settlement and rounding all sit inside the search rather than inside a formula. The identity is exact; the convention around it is a choice.

What the yield holds fixed

This identity prices a fixed coupon bond held to maturity, at the price you enter, with every coupon discounted at the same rate. Read as a forward-looking number it assumes each coupon can be put back to work at the yield itself, which is a real assumption rather than a footnote: a 7 percent yield realised in full needs 7 percent available on every $1,000 of coupon along the way. How yield to maturity works covers the reinvestment point in full. This is educational material, not financial advice.

Worked examples

A \$857.88 price with 10 years to run

A $1,000 face bond pays a 5 percent coupon in two payments a year, has 10 years to maturity, and trades at $857.88. What is the yield to maturity?

  1. Each coupon is 1000×0.05/2=251000 \times 0.05 / 2 = 25, and 10×2=2010 \times 2 = 20 of them are left.
  2. Find the rate that discounts those 20 coupons plus the $1,000 of face back to exactly $857.88.
  3. At 3.5 percent per half year, which is 7 percent a year, the discounted total is 857.88.

The yield to maturity is 7 percent on a $1,000 face bond bought at $857.88, well above the 5 percent coupon.

The same bond bought at par

Same $1,000 face, same 5 percent coupon, same 10 years, but now the price is $1,000. What is the yield?

  1. Paying $1,000 for a $1,000 face value means nothing is gained or lost at maturity.
  2. The only cash above the purchase price is the coupon stream, so the yield equals the coupon rate of 5 percent.

The yield to maturity is 5 percent. At par, coupon rate and yield are the same number, which is the only case where they are.

Quoting the coupon rate as the yield

The coupon rate answers what the issuer promised against face. It says nothing about what you paid. The same 5 percent coupon is 5.83 percent of a $857.88 price and 7 percent once the pull to $1,000 at maturity is counted. Three numbers, one bond, and only the last one is comparable to another bond.

Common questions

Why is the yield higher than the coupon rate here?

Because the bond was bought below face. The $857.88 price collects $1,000 at maturity, and that gain is part of the return.

Does yield to maturity assume coupons are reinvested?

Yes. One rate discounts every cash flow, which is the same as assuming each coupon earns that rate until maturity.

Is this financial advice?

No. It is educational material showing how price, coupon and yield fit into one identity.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.