Yield to Maturity Calculator
Calculate the Yield to Maturity (YTM) of a bond from its price, face value, coupon payment, and years to maturity.
Includes current yield, premium/discount analysis, and bond pricing rules.
Yield to Maturity (YTM) Formula
Yield to Maturity is the total annualized return you will earn by holding a bond from today until it matures — assuming all coupon payments are reinvested at the same rate.
Approximation Formula
Exact YTM requires iterative calculation, but the approximation is highly accurate:
YTM ≈ (Annual Coupon + (Face Value − Price) ÷ Years) ÷ ((Face Value + Price) ÷ 2)
Where:
- Annual Coupon = the fixed interest payment received each year
- Face Value = the amount paid back at maturity (typically $1,000)
- Price = current market price of the bond
- Years = years remaining to maturity
Three Yield Metrics Compared
Coupon Rate = Annual Coupon ÷ Face Value × 100 This is the rate printed on the bond certificate. It never changes.
Current Yield = Annual Coupon ÷ Current Price × 100 This reflects the income return at today’s price. It changes daily as price changes.
Yield to Maturity (YTM) = Includes coupon income + capital gain or loss at maturity. This is the most complete return measure — what you actually earn if you hold to maturity.
The Premium vs Discount Bond Rules
These rules always hold — they are mathematical certainties:
| Bond Price vs Face Value | Bond Type | YTM vs Coupon Rate |
|---|---|---|
| Price < Face Value | Discount Bond | YTM > Coupon Rate |
| Price = Face Value | Par Bond | YTM = Coupon Rate |
| Price > Face Value | Premium Bond | YTM < Coupon Rate |
Why? If you buy at a discount ($950 for a $1,000 bond), you receive the coupon PLUS a $50 capital gain at maturity. That gain boosts total return above the coupon rate.
Bond Price Sensitivity to Interest Rates
When interest rates rise, bond prices fall (and vice versa). The relationship is inverse and non-linear:
- Longer maturity bonds fall more than short maturity bonds for the same rate move.
- Lower coupon bonds fall more than high coupon bonds.
- This sensitivity is measured by Duration — a separate metric.
Worked Example
A bond with:
- Market Price: $950
- Face Value: $1,000
- Annual Coupon: $80
- Years to Maturity: 10
Step 1 — Current Yield:
Current Yield = $80 ÷ $950 = 8.42%
Step 2 — YTM Approximation:
YTM ≈ ($80 + ($1,000 − $950) ÷ 10) ÷ (($1,000 + $950) ÷ 2) YTM ≈ ($80 + $5) ÷ $975 YTM ≈ $85 ÷ $975 = 8.72%
Interpretation: The coupon rate is 8% ($80 ÷ $1,000). Since the bond trades at a discount ($950 < $1,000), YTM (8.72%) > Coupon Rate (8%) — exactly as the rule predicts.
Rate Comparison for This Bond
| Metric | Value | Meaning |
|---|---|---|
| Coupon Rate | 8.00% | Fixed rate printed on bond |
| Current Yield | 8.42% | Income return at current price |
| Yield to Maturity | 8.72% | Total return held to maturity |
Pro Tips
- YTM assumes you reinvest all coupons at the same YTM rate — unrealistic in practice. The realized compound yield will differ if rates change.
- When comparing bonds, always compare YTM — not coupon rate or current yield alone.
- U.S. Treasury YTM rates form the risk-free rate used in all other financial valuations.
- A bond’s YTM falling means its price is rising — often a sign the market expects interest rate cuts.