Bond Amount Estimator
Estimate the fair present value of a bond given its coupon rate, market yield, face value, and years to maturity.
Formula
Bond Price = (C / r) × [1 − (1 + r)−n] + F × (1 + r)−n
Where:
- C = Periodic coupon payment = (Annual Coupon Rate × Face Value) ÷ Frequency
- r = Periodic market yield = Annual Yield ÷ Frequency
- n = Total number of periods = Years to Maturity × Frequency
- F = Face (par) value of the bond
The first term is the present value of the annuity of coupon payments; the second term is the present value of the face value repaid at maturity. When the coupon rate equals the market yield, the bond prices at par (face value). When the coupon rate is below the market yield, the bond trades at a discount; above, at a premium.
Assumptions & References
- Coupons are paid at regular, equal intervals (ordinary annuity — end of period).
- The market yield (discount rate) remains constant over the life of the bond.
- The bond is priced on a coupon date (no accrued interest / clean price = dirty price).
- Face value is repaid in full at maturity (no default risk modelled).
- Current Yield = Annual Coupon Income ÷ Bond Price (does not account for capital gain/loss).
- For zero-yield scenarios the formula simplifies to: Price = (C × n) + F.
- Reference: Fabozzi, F.J. — Fixed Income Mathematics (4th ed.); CFA Institute curriculum.
- This tool provides an estimate only and does not constitute financial advice.