Bond Yield to Maturity (YTM) Calculator
Estimate a bond's yield to maturity using the standard approximation formula, plus its current yield, from face value, price, coupon, and years to maturity.
How to use this tool
- Enter the bond's face (par) value, usually $1,000.
- Enter the current price you would pay for the bond.
- Enter the annual coupon rate and years to maturity.
- Read the approximate YTM, current yield, and annual coupon payment.
- Compare YTM with the coupon rate to see if the bond trades at a discount or premium.
Yield to maturity captures a bond's full return — coupons plus any pull-to-par gain or loss — in one annual rate. Enter the face value, price, coupon, and years to estimate YTM and current yield.
Formula
Annual coupon = Face value × (Coupon rate ÷ 100).
Approximate YTM = [ Coupon + (Face − Price) ÷ n ] ÷ [ (Face + Price) ÷ 2 ], expressed as a percent, where n is years to maturity.
Current yield = (Annual coupon ÷ Price) × 100. Current yield ignores any gain or loss from holding the bond to maturity; YTM includes it.
How it works
Yield to maturity is the single annual rate that equates a bond's price to the present value of all its remaining coupon payments plus its face value at maturity. The exact YTM has no closed-form solution and is normally found by iteration, but the widely taught approximation used here is accurate enough for quick comparisons and intuition.
The approximation averages the annual coupon with the amortized capital gain or loss ((Face − Price) ÷ years) and divides by the average of face and price. A bond bought at a discount (price below face) has a YTM above its coupon rate because you also collect the pull-to-par gain; a bond bought at a premium has a YTM below its coupon rate. At par, YTM, current yield, and coupon rate all coincide.
This model assumes annual coupons, holding to maturity, no default, and no reinvestment assumption for received coupons. For exact figures — especially for semi-annual coupons, callable bonds, or tax effects — use a full bond-pricing routine. Reviewed by the AbraCalc Investing Desk. This tool provides general information, not investment advice; verify figures and consult a licensed professional before investing.
Worked example
$1,000 bond bought at $950, 5% coupon, 10 years to maturity
- Annual coupon = $1,000 × 5% = $50.00.
- Numerator = $50 + ($1,000 − $950) ÷ 10 = $50 + $5 = $55.
- Denominator = ($1,000 + $950) ÷ 2 = $975.
- Approximate YTM = ($55 ÷ $975) × 100 = 5.6410%.
- Current yield = ($50 ÷ $950) × 100 = 5.2632%.
Approximate YTM: 5.6410% — current yield 5.2632%, annual coupon $50.00.
How price relates to yield (5% coupon, $1,000 face, 10 years)
| Price | Trades at | YTM vs coupon |
|---|---|---|
| $950 | Discount | YTM above 5% coupon |
| $1,000 | Par | YTM equals 5% coupon |
| $1,050 | Premium | YTM below 5% coupon |
Key terms
- Yield to maturity (YTM)
- The total annualized return earned if a bond is bought at its current price and held until it matures.
- Current yield
- Annual coupon income divided by the bond's price; it ignores any gain or loss at maturity.
- Coupon rate
- The fixed annual interest a bond pays, stated as a percentage of its face value.
- Par value
- A bond's face value, the amount repaid at maturity — usually $1,000.
- Discount / premium
- A bond priced below par trades at a discount; above par it trades at a premium.
Frequently asked questions
- What is yield to maturity?
- YTM is the annual return you would earn by buying a bond at its current price and holding it to maturity, counting both coupon income and any gain or loss versus the face value.
- Why is this an approximation?
- Exact YTM requires solving for the rate that discounts all cash flows back to today, which has no algebraic solution and is found by iteration. The approximation formula is fast and close for most bonds.
- How does current yield differ from YTM?
- Current yield only counts coupon income relative to price. YTM also includes the gain or loss from the price converging to face value at maturity, so they match only when the bond trades at par.
- Why does a discount bond have a higher YTM?
- If you pay less than face value, you collect coupons plus an extra gain when the bond repays par at maturity, which raises the total return above the coupon rate.