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Finance Calc Kit
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Yield to Maturity Calculator

Calculate the yield to maturity (YTM) of bonds with exact IRR and approximate yield formulas.

Bond details

$
$
%

Exact yield to maturity (YTM)

5.7%

Semi-annual coupons until redemption at par ($1,000.00)

Approximate YTM

5.6%

Shortcut formula for quick estimates

Periodic coupon

$25.00

20 payments at semi-annual frequency

Total coupon income

$500.00

Sum of all coupon payments to maturity

Total return to maturity

$550.00

Coupons plus par minus $950.00 purchase price

How yield to maturity is calculated

YTM is the total annualized return if you hold the bond until it repays face value at maturity.

  1. 1. Build periodic cash flows to maturity

    You pay $950.00 today for a discount bond, receive $25.00 every semi-annual period, and $1,025.00 at maturity (20 periods).

  2. 2. Approximate YTM with the bond yield shortcut

    YTMapprox=C+F−PnF+P2\mathrm{YTM}_{approx} = \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}

    The approximation gives 5.6% using annual coupon $50.00 and 10 years to maturity.

  3. 3. Solve exactly with bisection

    P=∑t=1n−1C(1+r)t+C+F(1+r)nP = \sum_{t=1}^{n-1} \frac{C}{(1+r)^t} + \frac{C + F}{(1+r)^n}

    Bisection finds the periodic rate that prices the bond at $950.00, giving exact YTM of 5.7%.

Return breakdown at maturity

Purchase price

$950.00

Par at maturity

$1,000.00

Capital gain at maturity

$50.00

Total cash received

$1,500.00

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Understanding Yield to Maturity (YTM)

Yield to maturity is the total annualized return an investor earns by holding a bond until it repays face value at maturity, assuming all coupon payments are received on schedule and reinvested at the same yield. YTM accounts for coupon income plus any capital gain or loss between purchase price and par.

YTM is the standard benchmark for comparing bonds with different coupons, maturities, and prices. For callable bonds where early retirement is possible, also evaluate yield to call with our yield to call calculator. For full pricing, duration, and sensitivity analysis, use our bond calculator.

Exact YTM Formula

The exact yield to maturity solves for the periodic rate rr that equates market price to the present value of all coupon payments plus face value at maturity:

P=∑t=1n−1C(1+r)t+C+F(1+r)nP = \sum_{t=1}^{n-1} \frac{C}{(1+r)^t} + \frac{C + F}{(1+r)^n}

Where PP is the market price, CC is the periodic coupon, FF is face value (par), and nnis the total number of coupon periods to maturity.

Approximate YTM Shortcut

A widely used approximation estimates YTM without iterative solving:

YTMapprox=Cannual+F−PnyearsF+P2\mathrm{YTM}_{approx} = \frac{C_{annual} + \frac{F - P}{n_{years}}}{\frac{F + P}{2}}

Worked Example

A $1,000 par bond with a 5.00% annual coupon (paid semi-annually) trades at $950 with 10 years to maturity:

  • Periodic coupon: $25.00
  • Total periods: 20 semi-annual payments
  • Capital gain at maturity: $50.00 ($1,000 par minus $950 purchase)
  • Approximate YTM: about 5.64%
  • Exact YTM: about 5.5% to 6.0% (bisection on the full cash flow schedule)

Discount bonds (price below par) have YTM above the coupon rate because the investor earns coupon income plus a capital gain at maturity. Premium bonds behave the opposite way.

YTM vs Current Yield

Current yield divides annual coupon income by market price and ignores capital gains or losses at maturity. YTM is the more complete measure because it incorporates both coupon cash flows and the return of principal relative to purchase price.

Frequently asked questions

Why is YTM higher than the coupon rate on discount bonds?
When you buy below par, you receive the full face value at maturity plus coupons. The capital gain from discount to par boosts total return above the stated coupon rate.
What is the difference between exact and approximate YTM?
The approximate formula is a linear shortcut useful for quick estimates. Exact YTM uses bisection to solve the full present value equation and matches professional bond analytics.
Does YTM assume coupon reinvestment?
Yes. YTM implicitly assumes all coupon payments are reinvested at the same yield until maturity. In practice, reinvestment rates fluctuate, so realized return may differ.
How does semi-annual compounding affect YTM?
US bonds typically pay coupons twice per year. The periodic rate solved by bisection is a semi-annual rate, which is multiplied by 2 to express annual YTM on a bond-equivalent basis.
Are the results stored on a server?
No. All math runs in your browser. Nothing is sent to the server.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.