Bond Calculator
What is this bond worth? What's my yield? Calculate bond price from market yield, find YTM from current price, and understand why current yield and YTM differ.
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How to Use This Calculator
Tab "Bond Price"
Enter the bond's face value (typically 1,000), coupon rate (the stated annual interest), market yield (your required return or current market rate), and years to maturity. The calculator shows the fair price, whether the bond trades at a premium or discount, annual coupon income, and total return. The chart shows how price converges toward par as maturity approaches.
Tab "Yield to Maturity"
Enter the bond's face value, coupon rate, current market price, and years to maturity. The calculator solves for YTM iteratively — the single rate that equates all future cash flows to the current price. It also shows how YTM compares to current yield and explains the difference.
Tab "Current Yield vs YTM"
Enter the same four inputs as above. The calculator computes both current yield (income-only measure) and YTM (total return measure), and explains in plain language why they differ and which direction the gap runs depending on whether the bond trades at par, premium, or discount.
The Formulas
P = Σ [C / (1 + r)^t] + FV / (1 + r)^n
where C = annual coupon, r = market yield (decimal), FV = face value, n = years to maturity
Annual coupon:
C = FV × coupon rate
e.g. $1,000 × 5% = $50/year
Current yield:
CY = C / P = (FV × coupon rate) / current price
Yield to Maturity (YTM):
Solve for r in: P = Σ [C / (1 + r)^t] + FV / (1 + r)^n
No closed-form solution — this calculator uses Newton's method:
r_(n+1) = r_n − f(r_n) / f'(r_n), converging when |Δr| < 10^-10
Premium / discount / par:
Price > FV → Premium (coupon rate > market yield)
Price = FV → Par (coupon rate = market yield)
Price < FV → Discount (coupon rate < market yield)
All calculations assume annual coupon payments and redemption at face value at maturity. No accrued interest, transaction costs, or taxes are included. Results are universal pre-tax estimates.
Worked Examples
Example 1 — Bond Price: $1,000 face, 5% coupon, 4% market yield, 10 years → Premium
An investor wants to know the fair price of a bond paying 5% annually when the market yield is 4%. Because the coupon exceeds the market yield, the bond should trade above par.
Calculation: P = Σ(t=1 to 10) [$50 / (1.04)^t] + $1,000 / (1.04)^10 = $405.54 + $675.56 = $1,081.11. The investor pays $81.11 extra today in exchange for the above-market $50 coupon each year vs. the $40 a newly issued bond at 4% would pay.
Example 2 — YTM: $1,000 face, 4% coupon, bought at $950, 8 years → YTM = 4.76%
A bond with a 4% coupon trades at $950 — below its $1,000 face value. The investor wants to know their true annualised return if they hold to maturity.
YTM = 4.76% because the investor earns $40/year in coupon income AND gains $50 at maturity when the bond repays at $1,000. Newton's method solves: 950 = Σ(t=1 to 8) [40 / (1+r)^t] + 1000 / (1+r)^8 → r = 4.76%. The current yield (4.21%) understates the total return by ignoring the $50 capital gain.
Example 3 — CY vs YTM: 4.21% current yield vs 4.76% YTM — why they differ
Using the same bond from Example 2: $1,000 face, 4% coupon, trading at $950, 8 years to maturity.
The 0.55 pp gap exists entirely because CY only counts the $40 annual coupon income. YTM also counts the $50 capital gain you receive at maturity ($1,000 redemption vs $950 purchase), spread over 8 years. Rule: discount bond → YTM > CY; premium bond → YTM < CY; bond at par → YTM = CY.
Understanding Bond Valuation: Key Concepts
The Price-Yield Relationship
Bond price and yield move in opposite directions — this is the most important rule in fixed income. When market interest rates rise, new bonds offer higher coupons, making existing bonds less attractive. Their prices fall until the effective yield matches the market. The reverse happens when rates fall: existing bonds with higher coupons become desirable and their prices rise above par.
Coupon Rate vs Market Yield vs YTM
Three different "rates" describe a bond:
| Rate | What it measures | Fixed or variable? |
|---|---|---|
| Coupon rate | Annual coupon as % of face value — the income you receive | Fixed (set at issue) |
| Current yield | Annual coupon / current price — income return only | Variable (price changes) |
| YTM | Total annualised return if held to maturity (income + capital) | Variable (price changes) |
When comparing bonds, always use YTM — it is the only measure that accounts for the full economics of holding a bond to maturity.
Duration and Interest Rate Risk
Longer-maturity bonds are more sensitive to yield changes than shorter ones. A 30-year bond's price will swing much more than a 2-year bond's for the same 1% yield movement. This sensitivity is formalised as duration (measured in years) and modified duration (% price change per 1% yield change). Higher duration = more interest rate risk.
Premium Bond Pull-to-Par
A bond bought at a premium will gradually lose that premium as it approaches maturity — a process called pull-to-par or amortisation of premium. Every year, the premium erodes until the bond trades at exactly face value on the maturity date. The price chart in the Bond Price tab visualises this convergence.
Zero-Coupon Bonds
A bond with a 0% coupon rate (set coupon rate = 0) is a zero-coupon bond. It pays no periodic interest and is always priced at a deep discount. All return comes from the difference between purchase price and face value at maturity. YTM equals the implicit annualised return: P = FV / (1 + r)^n.
Frequently Asked Questions
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