Bond Yield to Maturity (YTM) Calculator
Solve for a bond's yield to maturity from face value, coupon rate, market price, and years to maturity using a numerical (Newton-Raphson) solver. Educational. Runs in your browser.
Yield to maturity is the single annual discount rate that makes the present value of all the bond's coupon payments plus its face value at maturity equal to its current market price. There is no closed-form solution, so it is found numerically (Newton-Raphson here). When price equals face value, YTM equals the coupon rate; below par, YTM exceeds the coupon (and vice versa). Current yield ignores the gain or loss to par, so it differs from YTM for any bond not trading at par. Educational; everything runs in your browser.
About this tool
Yield to maturity (YTM) is the total annualized return an investor earns by buying a bond at its current market price and holding it until maturity, assuming every coupon is paid on time and reinvested at the same rate. It is the bond market's standard measure of return because it folds three things into one number: the coupon income, and the gain or loss between the purchase price and the face value repaid at maturity. Mathematically, YTM is the discount rate that sets the present value of all future cash flows — every coupon payment plus the face value at the end — equal to the bond's current price. That equation cannot be rearranged to solve for the rate directly, so YTM has to be found numerically; this tool uses the Newton-Raphson method (with a bisection fallback for safety) to converge on the rate that prices the bond correctly. A few relationships are worth knowing: a bond trading at par (price equal to face value) has a YTM equal to its coupon rate; a bond trading below par (a discount) has a YTM above its coupon rate, because the buyer also gains as the price rises to par; and a bond above par (a premium) has a YTM below its coupon rate. YTM differs from the simpler 'current yield' (annual coupon ÷ price), which ignores the pull toward par. This is educational and assumes no default and constant reinvestment. Everything runs in your browser; nothing is uploaded.
How to use it
- Enter the bond's face (par) value — usually 1,000.
- Enter the annual coupon rate as a percentage.
- Enter the current market price you would pay.
- Enter years to maturity and the coupon frequency.
- Read the yield to maturity; compare it to the coupon rate and current yield.
Frequently asked questions
- What is yield to maturity?
- YTM is the annualized total return from holding a bond to maturity, accounting for coupon income plus any gain or loss between purchase price and face value. It is the discount rate that makes the present value of all cash flows equal the current price.
- Why is YTM solved numerically?
- The bond pricing equation cannot be algebraically rearranged to isolate the yield, so there is no closed-form formula. Methods like Newton-Raphson iterate toward the rate that prices the bond exactly — which is what this calculator does.
- How does YTM relate to the coupon rate?
- At par (price = face value) YTM equals the coupon rate. Below par (a discount), YTM is higher than the coupon rate; above par (a premium), YTM is lower. The difference reflects the gain or loss as the price converges to par at maturity.
- How is YTM different from current yield?
- Current yield = annual coupon ÷ price and ignores the pull toward par. YTM includes that capital gain or loss and the time value of every cash flow, so the two are equal only for a bond trading at par.
- What assumptions does YTM make?
- It assumes the issuer makes every payment (no default) and that coupons are reinvested at the YTM itself. Real reinvestment rates vary, so realized return can differ — this is reinvestment risk.
- Is anything uploaded?
- No. The solver runs entirely in your browser.