Bond Pricing / Yield Calculator
Price a bond from yield, or approximate yield from price.
Overview
A bond pricing and yield calculator translates between a bond's price and the discount rate (yield) implied by that price. Bonds promise a fixed schedule of coupon payments plus a face-value return at maturity. The market price moves inversely to yields: when prevailing rates rise, existing bonds with lower coupons trade at a discount; when rates fall, those bonds trade at a premium. Knowing both numbers is essential when comparing two bonds with different coupons or maturities.
This calculator solves either direction. Given a yield to maturity, it discounts every cash flow back to today to produce a clean price. Given a target price, it iterates on yield until the present value of the cash flows matches that price, giving an approximate yield to maturity. The math treats the bond as if held to maturity with all coupons received on schedule; it ignores credit risk, call provisions, taxes, and reinvestment rate assumptions.
How it works
Price is the sum of discounted cash flows: P = Σ (C / (1 + y/m)^t) + F / (1 + y/m)^N where C is the periodic coupon, y is the annual yield, m is compounding periods per year, F is face value, and N is the total number of periods. The coupon C equals face × coupon_rate / m. For the reverse direction the tool runs a bisection or Newton-Raphson search on y until the computed price is within a small tolerance of the entered market price, since yield cannot be solved algebraically for bonds with more than one period remaining.
Examples
- A 10-year, $1,000 face bond with a 5% annual coupon paid semi-annually, yielding 6%: each coupon is $25, discounted over 20 periods at 3% per period — price comes out near $925.61, a discount because the coupon undershoots market yield.
- The same bond priced at par ($1,000) implies a 5% yield — coupon equals yield, no premium or discount.
- A 5-year, $10,000 zero-coupon bond at a 4% annual yield prices at
10000 / 1.04^5 ≈ $8,219.27. - A bond trading at $1,050 with a 6% coupon and 8 years left typically implies a yield around 5.25% — solved iteratively because there is no closed form.
FAQ
What's the difference between current yield and YTM?
Current yield is just coupon divided by price. Yield to maturity also bakes in the capital gain or loss versus face value over the remaining life.
Why does my bank quote a different price?
Dealer quotes include bid-ask spreads, accrued interest (dirty vs clean price), and sometimes day-count conventions other than 30/360.
Does this handle callable bonds?
No — it assumes the bond is held to maturity. Callable bonds require yield-to-worst, which solves the lowest yield across all call dates.
What compounding frequency should I use?
Match the bond's actual coupon schedule: semi-annual for most US Treasuries and corporates, annual for many European issuers.
Is this a substitute for a Bloomberg terminal?
No. Treat it as an educational sanity check, not an execution price.