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Bond Calculator (YTM)

Calculate Yield to Maturity for any bond from face value, coupon rate, market price, and years to maturity. Free, instant, and accurate.

✓ Tested formula & cited sources Checked against independent sources · Oct 18, 2026 Private: runs in your browser

The bond's redemption value at maturity. Standard US corporate and Treasury bonds: $1,000.

The stated annual interest rate printed on the bond. A $1,000 bond at 5% pays $50/year.

The price the bond is currently trading at on the secondary market. Can be above or below face value.

Number of years until the bond matures and you receive the face value.

How often the bond pays interest. US bonds typically pay semi-annually.

Results

Yield to Maturity (YTM)

5.6617%

YTM is the total return if you hold to maturity and reinvest every coupon at this same rate — that reinvestment assumption is the weak link, since real rates move. The bond is trading at a discount to face value, which is why YTM runs above the coupon rate.

Current Yield (Annual Coupon ÷ Market Price)
5.2632%
Bond Trading Status
Discount — $50.00 (5.00%) below par
Annual Coupon Income (Semi-Annual payments of $25.00)
$50.00
Total Coupon Income Over Life
$500.00
Capital Gain at Maturity
+$50.00
Total Absolute Return (Coupons + Capital)
$550.00
YTM vs. Coupon Rate
YTM (5.6617%) > Coupon (5.0000%) — Discount bond confirms higher effective yield

The formula

YTM Approximation: (Annual Coupon + (Face − Price) / Years) / ((Face + Price) / 2) · Exact YTM: solved by bisection (binary search)

YTM
Yield to Maturity
Current Yield
Current Yield
Discount vs Premium
Discount & Premium Bonds
Duration
Macaulay Duration

Worked example — Face / Par Value 1000, Annual Coupon Rate 5.00 %, Current Market Price 950, Years to Maturity 10 years

Yield to Maturity (YTM) = 5.6617%

Full explanation ↓

How Bond Calculator (YTM) Works

YTM Approximation: (Annual Coupon + (Face − Price) / Years) / ((Face + Price) / 2) · Exact YTM: solved by bisection (binary search)

The Yield to Maturity is the internal rate of return (IRR) of all future cash flows discounted back to the current price. There is no closed-form algebraic solution — it requires iterative numerical methods. This calculator uses binary search until the discounted cash flows match the market price to within $0.0001. It assumes you buy on a coupon date, so accrued interest is ignored, years to maturity multiplied by payments per year is rounded to a whole number of coupon periods, and the yield is quoted on a bond-equivalent basis (periodic yield × payments per year).

YTM
Yield to Maturity — The annualized total return if you buy the bond at the current market price and hold it until maturity, assuming all coupons are reinvested at the same YTM rate. This is the single most important metric for bond comparison — it accounts for the coupon income, capital gain or loss, and time value of money.
Current Yield
Current Yield — Annual coupon payment divided by current market price. A simpler but less accurate measure than YTM — it ignores the capital gain/loss at maturity. A $1,000 bond at a 5% coupon rate trading at $950 has a current yield of $50/$950 = 5.26%, but a higher YTM that also captures the $50 capital gain at maturity.
Discount vs Premium
Discount & Premium Bonds — A bond trades at a discount when market price is below face value (YTM > coupon rate) and at a premium when price is above face value (YTM < coupon rate). The difference between market price and face value represents the capital gain or loss at maturity.
Duration
Macaulay Duration — A measure of interest rate sensitivity expressed in years. Higher duration = higher price volatility when rates change. A 10-year, 5% semi-annual coupon bond priced at par has a Macaulay duration of about 8.0 years and a modified duration of about 7.8 — meaning a 1% rate rise causes roughly a 7.8% price decline.
Bonds pay fixed coupon income over time plus return of face value at maturity — YTM accounts for both income and capital gain or loss

Understanding the Result

Bond pricing and yield have an inverse relationship — the most fundamental concept in fixed income: when market interest rates rise, existing bond prices fall (and vice versa). If you paid $1,000 for a 5% coupon bond and rates rise to 7%, your bond becomes less attractive — it must drop in price until its effective yield (YTM) rises to compete with the 7% market rate. This calculator makes that relationship explicit: enter any price below par and watch the YTM rise above the coupon rate.

Enter any price above par and watch the YTM fall below it.

How to Use

  1. Enter the face value (usually $1,000 for US bonds), coupon rate, and current market price, plus years to maturity and payment frequency.
  2. The calculator shows YTM, current yield, and whether the bond trades at a discount or premium.
  3. Use YTM — not coupon rate or current yield — to compare bonds with different prices and coupon structures.

Frequently Asked Questions

What is the difference between YTM and current yield?
Current yield = annual coupon / market price. It is simple to calculate but ignores the capital gain (if you bought at a discount) or loss (if you bought at a premium) at maturity. YTM is the complete measure — it incorporates all cash flows including the final return of face value. For a bond at par, current yield = YTM = coupon rate. For any other price, all three are different.
Why does bond price move inversely to interest rates?
When market rates rise, newly issued bonds offer higher coupons. To compete, the price of existing lower-coupon bonds must fall until their total return (YTM) matches the new market rate. Conversely, when rates fall, the higher fixed coupon of existing bonds becomes more valuable, so their price rises. This inverse relationship is the central risk of bond investing — "interest rate risk."
What is bond duration and why does it matter?
Duration measures how sensitive a bond's price is to interest rate changes — roughly, the percentage change in price for a 1% change in yield. A 10-year bond with 5-year duration would drop approximately 5% in price if yields rise 1%. Longer maturity and lower coupon rates increase duration (higher rate sensitivity). Zero-coupon bonds have the highest duration (equal to their maturity).
What is the YTM approximation formula?
The classic approximation: YTM ≈ (Annual Coupon + (Face Value − Market Price) / Years to Maturity) / ((Face Value + Market Price) / 2). This is the formula taught in most finance courses and produces a close estimate. This calculator uses an iterative binary search to find the exact YTM (price match within $0.0001).
What is a zero-coupon bond and how is it different?
A zero-coupon bond pays no regular coupon payments — it is issued at a deep discount to face value and matures at par. The total return comes entirely from capital appreciation. Zero-coupon bonds have higher duration (equal to maturity) and thus higher price volatility relative to coupon-paying bonds of the same maturity. They are popular for tax-advantaged accounts and for matching specific future liabilities.

Common Uses

  • •Calculate the yield to maturity on a bond trading at a discount or premium to determine its true return versus the coupon rate.
  • •Compare bonds with different coupon rates, maturities, and market prices to find the best fixed-income investment for your portfolio.
  • •Understand how changes in market interest rates affect the price of your existing bond holdings and their effective yield.

Sources

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Cite this calculator

TheCalcUniverse. "Bond Calculator — Yield to Maturity (YTM) & Pricing." TheCalcUniverse, 2026, https://thecalcuniverse.com/finance/bond-calculator/. Accessed October 25, 2026.

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