Bond Calculator
Price a bond and compute current yield, yield to maturity and duration.
About Bond Calculator
A bond's price is the present value of all future coupon payments plus the par value redemption, discounted at the required yield. When yield exceeds the coupon rate the bond trades at a discount (below par); when yield is below the coupon rate it trades at a premium. Yield to Maturity is the single discount rate that makes all future cash flows equal the current price — solving for it requires iteration. Macaulay Duration is the weighted average time to receive cash flows and measures interest rate sensitivity.
Formulas
Bond price
Price = Σ [C / (1+r)^t] + F / (1+r)^n
- C
- Coupon payment per period
- r
- Periodic yield (YTM / payments per year)
- n
- Total periods
- F
- Face (par) value
Macaulay Duration
Duration = Σ [t × PV(cash flow at t)] / Bond Price
- t
- Time period (in years)
- PV(CF_t)
- Present value of cash flow at time t
- P
- Bond price
Worked example
With the default values below, Bond Calculator returns Bond Price of $1,081.7572. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Face Value (Par)minimum 1 $
- 1,000 $
- Coupon Rate (% per year)accepts 0–30
- 5
- Coupon Payments per Yearone of Semi-annual (2×/year), Annual (1×/year), Quarterly (4×/year), Monthly (12×/year)
- Semi-annual (2×/year)
- Years to Maturityaccepts 0.25–100
- 10
- Calculateone of Bond Price (given YTM), Yield to Maturity (given Price)
- Bond Price (given YTM)
- Market Yield / Required Return (% per year)accepts 0–50
- 4
- Market Priceminimum 1 $
- 950 $
Results
- Bond Price
- $1,081.7572
- Yield to Maturity (YTM)
- 4.0000%
- Current Yield
- 4.6221%
- Annual Coupon Payment
- $50.00
- Macaulay Duration (years)Weighted average time to receive the bond's cash flows.
- 8.0809
- Modified DurationPrice sensitivity: a 1% rate rise lowers price by approx. modified duration %.
- 7.9225
- Premium / (Discount)Positive = trading above par; negative = below par.
- $81.7572
Step by step
- 1Annual coupon= $50.00
- 2Coupon per period= $25.0000
- 3Bond price (sum of discounted cash flows)= $1,081.7572
- 4Current yield= 4.6221%
- 5Macaulay duration= 8.0809 yearsWeighted average time to receive cash flows
Assumptions and limits
- The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
- This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why does a bond's price fall when interest rates rise?
A bond locks in fixed coupon payments. If new bonds issue at a higher rate, your lower-coupon bond is less attractive, so its price must fall until the effective yield (YTM) matches the new market rate. The relationship is inverse and quantified by duration.
What is the difference between YTM and current yield?
Current yield is simply the annual coupon divided by the current price — it ignores capital gain/loss at maturity. YTM accounts for the price difference from par, amortising it over the remaining life. For bonds trading at par they are equal; for discounted bonds YTM > current yield.
What is Macaulay Duration used for?
Duration measures interest rate risk. A bond with 7 years Macaulay Duration loses approximately 7% × Δ(yield) in price for each percentage-point rise in rates (more precisely, Modified Duration gives this sensitivity). It also equals the holding period at which price risk and reinvestment risk cancel out.
What is a 'clean' vs 'dirty' bond price?
The price this calculator gives is the 'dirty' (full) price including accrued interest. In practice bonds are quoted at the 'clean' price and accrued interest is added at settlement. For most educational and financial planning purposes the dirty price is what matters.