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Bond Calculator
Price and yield move as one. This bond calculator prices a fixed-coupon bond from its market yield or solves yield to maturity from a price — adding the current yield, duration and convexity most tools skip. Ordinary coupon bonds only, not Treasury savings bonds.
See how this works on a $1,000 bond with a 5% coupon — 3 real examples
Bond price
Par$0
Clean price on a coupon date — no accrued interest.
Yield to maturity
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Current yield
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Modified duration
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Convexity
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Price vs. yield
How this bond's price changes as the market yield moves — the curve's steepness is its duration, and its bend is convexity.
Coupon scheduleEvery cash flow to maturity
| Period | In (yrs) | Coupon | Principal | Total cash flow |
|---|
How this bond's price and yield are calculated
A bond's price is the present value of its coupons plus its face value, discounted at the per-period yield:
Price = C · (1 − (1 + y)−n) / y + F · (1 + y)−n
C = coupon per period y = yield / periods n = years × periods
where F is the face value and C is F × coupon rate / periods. To solve for yield to maturity, the calculator inverts this formula numerically — it searches for the per-period yield that reprices the bond to your entered price, then annualizes it by multiplying by the number of periods. Current yield is the annual coupon divided by price. Macaulay duration is the cash-flow-weighted average time to maturity in years; modified duration is Macaulay ÷ (1 + y) and estimates the percentage price change per 1-point yield move; convexity is the second-order term that corrects for the curve's bend.
Assumptions: this is clean, coupon-date pricing — the bond is valued as if today is a coupon date, so there is no accrued interest, settlement date or dirty price. Coupons are assumed constant and reinvested at the yield to maturity, and the number of periods is rounded to a whole coupon. It prices ordinary fixed-coupon bonds; it is not a Treasury EE/I savings-bond value lookup, which uses separate government redemption tables.
One bond, three market yields
The same $1,000 bond — 5% coupon, ten years, paid twice a year — priced when the market demands 6%, 5% and 4%.
Rates above the coupon: a 6% market
market price$925.61
- Newer bonds pay 6%, so this 5% coupon only finds a buyer at $74.39 below face value.
- The $50 a year in coupons works out to a 5.40% current yield at this price.
- A modified duration of 7.67 years says a 1-point yield rise costs roughly 7.7% of the price.
Buying at a discount is what lifts a 5% coupon up to the 6% the market demands.
Load this example (opens in a new tab)Coupon equals market: priced at par
market price$1,000.00
- With the coupon and the market rate both at 5%, the bond changes hands at exactly face value.
- Current yield and yield to maturity agree at 5.00% — no discount or premium to unwind.
- Modified duration lands at 7.79 years, sitting between the 6% and 4% cases.
Par is the balancing point: the price where the coupon already pays what buyers ask.
Load this example (opens in a new tab)Rates below the coupon: a 4% market
market price$1,081.76
- A 5% coupon beats what new bonds offer, and buyers bid $81.76 over face value for it.
- Paying the premium trims the same $50 coupon stream to a 4.62% current yield.
- From 6% down to 4%, a two-point drop in market yield moves the price by $156.15.
Price and yield pull in opposite directions — this side of the seesaw favors the seller.
Load this example (opens in a new tab)Illustrations only, not financial advice. Your own rate, taxes and insurance will differ — check with a qualified financial advisor before acting on any of this.
Reading a bond's price, yield and duration
- Price and yield move opposite ways. Type a higher market yield and the price drops; that inverse link is the whole reason bonds lose value when rates rise.
- Coupon vs. yield tells you premium or discount. Coupon above yield → premium (price over par); coupon below yield → discount; equal → par. The badge on your result names it.
- Current yield isn't the full return. It only counts coupons against price. Yield to maturity also captures the pull-to-par gain or loss, so it's the number to compare bonds on.
- Duration is your rate-risk gauge. A modified duration of 8 means roughly an 8% price swing for a 1-point yield move — longer maturities and lower coupons raise it.
- Convexity works in your favor. Because the price-yield line curves, real losses are a little smaller and gains a little larger than duration alone predicts.
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Frequently asked questions
How do you price a bond?
A bond price is the present value of every future cash flow — each coupon plus the face value at maturity — discounted at the market yield. This bond price calculator uses Price = C·(1−(1+y)⁻ⁿ)/y + F·(1+y)⁻ⁿ, where C is the coupon per period, y the yield per period and n the number of periods. A $1,000 bond with a 5% coupon paid semiannually for 10 years, priced to a 6% yield, works out to about $925.61 — a discount, because its coupon is below the market rate.
What is yield to maturity (YTM)?
Yield to maturity is the single annualized rate that makes a bond’s price equal the present value of all its remaining coupons and its face value — the total return you’d earn holding it to maturity, assuming coupons are reinvested at that same rate. Switch this yield to maturity calculator to “Solve for yield,” type the market price, and it finds the YTM by solving the price formula for y.
What is the difference between the coupon rate and the yield?
The coupon rate is fixed against face value — a 5% coupon on a $1,000 bond always pays $50 a year. Yield reflects your actual return based on what you pay: current yield is annual coupon ÷ price, and yield to maturity also folds in the gain or loss between your price and the $1,000 you receive at maturity. When a bond trades below par, its yield is higher than its coupon rate; above par, lower.
What happens to bond prices when interest rates rise?
Bond prices fall when market rates rise, because a fixed coupon becomes less attractive than newly issued bonds paying more. The size of the move is captured by bond duration: a modified duration of 7 means a 1-percentage-point rise in yields drops the price about 7%. Longer maturities and lower coupons have higher duration, so they swing more. The price-vs-yield curve above shows this relationship for your bond.
What is bond duration and convexity?
Modified duration estimates the percentage price change for a 1-percentage-point change in yield — it’s the bond’s interest-rate sensitivity in a single number. Macaulay duration, measured in years, is the weighted-average time until you receive the bond’s cash flows. Convexity is the second-order correction: because the price-yield relationship curves, duration alone slightly overstates losses and understates gains, and convexity accounts for that bend.
Why does a bond trade at a premium or a discount?
It comes down to how the coupon compares with the market yield. When the coupon rate is higher than the yield investors demand, the bond is worth more than its face value and trades at a premium; when the coupon is lower, it trades at a discount below par. When they’re equal, the bond is priced exactly at par. This calculator flags which case you’re in on every result.
Does this calculator include accrued interest or savings-bond values?
No. It prices generic coupon bonds on a coupon date using the clean price — no accrued interest, settlement date or dirty price — which is the standard way to compare bond valuations. It is not a Treasury EE/I savings-bond value lookup; those follow separate government redemption tables. Use this as a bond price, yield to maturity and duration calculator for ordinary fixed-coupon bonds.
Disclaimer: these calculators are educational tools, not financial advice. They model your inputs with published formulas, but they cannot know your full situation — for decisions with real stakes, talk to a qualified professional. Formulas and defaults last reviewed .