Bond Calculator
Price a bond and compute current yield, yield to maturity and duration.
Inputs
Annual coupon as % of face value.
Bond Price
$1,081.7572
Yield to Maturity (YTM)
4.0000%
Current Yield
4.6221%
Annual Coupon Payment
$50.00
Macaulay Duration (years)
8.0809
Weighted average time to receive the bond's cash flows.
Modified Duration
7.9225
Price sensitivity: a 1% rate rise lowers price by approx. modified duration %.
Premium / (Discount)
$81.7572
Positive = trading above par; negative = below par.
Step by step
Annual coupon
$1,000.00 × 5%
= $50.00
Coupon per period
$50.00 ÷ 2
= $25.0000
Bond price (sum of discounted cash flows)
= $1,081.7572
Current yield
$50.00 ÷ $1,081.7572
= 4.6221%
Macaulay duration
= 8.0809 years
Weighted average time to receive cash flows
Cash flow schedule (first 40 periods)
| Period | Cash Flow | Present Value |
|---|---|---|
| 1 | $25.00 | $24.51 |
| 2 | $25.00 | $24.03 |
| 3 | $25.00 | $23.56 |
| 4 | $25.00 | $23.10 |
| 5 | $25.00 | $22.64 |
| 6 | $25.00 | $22.20 |
| 7 | $25.00 | $21.76 |
| 8 | $25.00 | $21.34 |
| 9 | $25.00 | $20.92 |
| 10 | $25.00 | $20.51 |
How it works
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
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.