Bond Price Calculator
Price bonds, build full amortization schedules, and understand premium vs. discount dynamics — with step-by-step explanations for both straight-line and effective interest methods.
Background
A bond's price depends on its coupon rate relative to the prevailing market rate. When the coupon rate exceeds the market rate, the bond sells at a premium; when it falls short, the bond sells at a discount; when they match, the bond prices at par. This calculator supports pricing from inputs, solving for yield-to-maturity, and generating complete amortization schedules under both methods.
How to use this calculator
- Choose Price a bond to find the fair value price from face value, coupon rate, market rate, and maturity.
- Use Yield to maturity when you know the current market price and want to solve for the implied return.
- Use Amortization schedule to see the full period-by-period interest expense, amortization, and carrying value table.
- Use Compare methods to see straight-line and effective interest side-by-side for the same bond.
- Click any quick example chip to instantly load a pre-built scenario.
How this calculator works
Bond price is calculated as the present value of all future cash flows: the stream of coupon payments plus the par value at maturity, each discounted at the market (required) rate per period. When the coupon rate is below the market rate, this produces a price below par (discount bond). When above, it produces a price above par (premium bond).
For YTM, the calculator uses Newton-Raphson iteration to find the discount rate that makes the present value of all cash flows equal to the known market price. For amortization, effective interest applies the market rate to the current carrying value each period; straight-line spreads the total premium or discount evenly over all periods.
Formulas & Equations Used
Bond price: P = C × [1 − (1 + r)⁻ⁿ] / r + FV × (1 + r)⁻ⁿ
Effective interest expense: Interest = Carrying Value × Market Rate per period
Straight-line amortization: Amortization = (Face − Price) / Total periods
Carrying value (effective): CV = Prior CV + (Interest − Coupon payment)
Where: C = coupon payment per period, r = market rate per period, n = total number of periods, FV = face value.
Example Problems & Step-by-Step Solutions
Example 1: Discount bond
A \$1,000 bond with an 8% annual coupon, 5-year maturity, and a market rate of 10% (semi-annual). Because the coupon rate is below the market rate, the bond prices below par — investors pay less to compensate for the lower coupon income.
Example 2: Premium bond
Same bond with a 10% coupon vs. an 8% market rate. The coupon exceeds what the market requires, so investors bid the price above par — the extra coupon income is worth paying a premium for.
Example 3: Effective interest amortization
Under the effective interest method, interest expense in each period = the carrying value × the market rate. This keeps the effective yield constant across all periods, which is the theoretically correct approach under GAAP and IFRS.
Example 4: Straight-line amortization
Straight-line amortization spreads the total discount or premium evenly across all periods. It is simpler to apply but distorts the effective interest rate over time. GAAP permits it only when results are not materially different from effective interest.
Frequently Asked Questions
Why does a bond sell at a discount?
When the coupon rate is lower than the market (required) rate, investors demand a price below par to earn a competitive return. The discount gradually amortizes to zero as the bond approaches maturity.
Which amortization method is required under GAAP?
GAAP requires the effective interest method unless the straight-line results are not materially different. IFRS also requires effective interest. Both methods produce the same total interest expense over the bond's life.
What is yield to maturity (YTM)?
YTM is the discount rate that equates the present value of all future cash flows to the bond's current market price. It represents the total annualized return an investor earns if they hold the bond to maturity.
What happens to price as a bond approaches maturity?
Regardless of whether the bond was issued at a discount or premium, its carrying value converges to face value at maturity. This is called the "pull to par" effect, and the amortization schedule shows this convergence period by period.
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