Complete suite: bond price, YTM (yield to maturity), current yield, BEY (bond equivalent yield), duration & convexity — with per-period cash flow tables and price sensitivity to yield changes.
P = Σ coupon/(1+y)t + F/(1+y)n — the present value of all cash flows discounted at the YTM.
Follows the Bond Price tab inputs. PV is computed with the per-period YTM.
| Period | Coupon | Principal | Cash flow | Discount factor | Present value (PV) |
|---|
Follows the Bond Price tab inputs. Shows the inverse price–yield relationship.
| YTM | Price | Change vs initial YTM |
|---|
A bond price calculator computes the fair (present) value of a bond from all of its future cash flows: periodic coupon payments plus the return of face value at maturity, all discounted at the market-required yield. The formula is P = Σ coupon/(1+y)^t + F/(1+y)^n, where y = yield per period and n = number of periods. This calculator runs 100% in your browser — no data is sent to any server.
YTM is the annualized return you earn if you buy a bond at its current market price and hold it to maturity, assuming all coupons are paid on time and reinvested at the same rate. Mathematically, YTM is the discount rate that makes the present value of all the bond's cash flows exactly equal to its market price — computed here with a robust bisection method.
Current yield = annual coupon ÷ market price × 100%. This measure is simple: it only compares this year's coupon income with the price you pay. Example: a 1,000 face-value bond with a 6% coupon (60 per year) priced at 1,043.76 has a current yield of 60 ÷ 1,043.76 = 5.75%. Unlike YTM, current yield ignores any capital gain or loss at maturity and the time value of money.
BEY is the yield expressed as an annual rate with semiannual compounding (semiannual APR), so yields from different payment frequencies can be compared apples-to-apples. This calculator uses the standard definition BEY = 2 × [(1 + y/m)^(m/2) − 1], where y = annual nominal yield and m = compounding frequency per year. Example: a 5% nominal yield with quarterly compounding equals a BEY of 5.03125%. For effective annual yield, use BEY = 2 × (√(1 + y_effective) − 1).
Duration measures the weighted-average time to receive a bond's cash flows, and at the same time its price sensitivity to yield changes. Macaulay duration = Σ t × PV(CF_t) ÷ price, expressed in years. Modified duration = Macaulay ÷ (1 + y/m), and gives a practical estimate: price changes by about −modified duration × yield change. Example reference bond (5 years, 6% semiannual coupon, 5% YTM): Macaulay duration 4.41 years and modified duration 4.30 years, so a 1% yield increase is estimated to lower the price by about 4.30%.
Convexity measures the curvature of the price-yield relationship: how fast duration itself changes as yield moves. Because the relationship is curved (convex), a yield decline raises the price more than an equal-sized yield increase lowers it. Our reference bond's convexity is 22.08 (years²). The practical rule: at the same price and yield, a higher-convexity bond benefits more when yield volatility is large.
Because price is the present value of fixed cash flows discounted at the yield. When yield rises, the discount factor grows, so the present value of each payment shrinks — price falls, and vice versa. A real example from this calculator: a 5-year bond, 1,000 face value, 6% annual coupon paid semiannually (30 per period). At 5% YTM it is priced at 1,043.76. If market yield rises to 7%, the price drops to 958.42; if yield falls to 3%, the price rises to 1,138.33.
Premium (price above face value): when the coupon rate is higher than the market yield — in the example above, a 6% coupon vs 5% YTM gives a price of 1,043.76. Discount (price below face value): when the coupon is lower than the market yield. Par (price equals face value): when the coupon exactly equals the market yield. This relationship follows directly from the pricing formula: the larger the yield in the denominator (1+y)^t, the smaller the present value of each cash flow.
Current yield only looks at this year's coupon divided by the market price (example: 5.75% on the reference bond) — simple but ignores what happens at maturity. YTM is the total annualized return to maturity assuming coupon reinvestment (example: 5.00%) — the most complete measure for comparison. BEY is the yield normalized to a semiannual-compounding basis (example: a 5% quarterly yield equals a BEY of 5.03125%) — useful for comparing bonds with different coupon frequencies.
With the same annual coupon and annual YTM, more frequent payments (semiannual, quarterly, monthly) produce a slightly higher price, because some cash is received earlier and discounted less. The effect is small but measurable — which is exactly why BEY is needed for fair comparisons across frequencies.
No. All figures on this page are educational estimates for understanding bond math — not financial advice and not investment recommendations. This model uses simple assumptions (coupons always paid in full, no default risk, no taxes or fees, flat yield curve) that rarely match real market conditions exactly. For decisions involving real money, consult a licensed financial planner.
Five inputs: (1) face value, (2) annual coupon rate, (3) coupon payment frequency — annual, semiannual, quarterly, or monthly, (4) term to maturity in years, and (5) the desired YTM or market discount rate. In YTM mode, the fifth input is replaced by the bond's market price, and the calculator then solves for its yield using bisection.
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