Bond Yield Calculator

Bond Yield to Maturity (YTM) is the total return an investor earns if a bond is held until it matures and all coupon payments are reinvested at the same rate. It is the single most important metric for comparing bonds of different prices, coupon rates, and maturities.

Approximate YTM formula: YTM ≈ (Annual Coupon + (Face Value − Market Price) ÷ Years to Maturity) ÷ ((Face Value + Market Price) ÷ 2)

Exact YTM is found by solving the price equation iteratively (requires a financial calculator or numerical methods): Market Price = Σ(Coupon ÷ (1+YTM)^t) + Face Value ÷ (1+YTM)^n

What each variable means:

• Face Value (Par Value): the amount the bond pays at maturity. Typically $1,000 per bond.
• Market Price: what the bond currently trades for. Can be above par (premium) or below par (discount).
• Annual Coupon = Face Value × Coupon Rate. A 5% coupon on a $1,000 bond = $50/year.
• Years to Maturity (n): time remaining until the bond matures.
• YTM: the discount rate that equates the present value of all future cash flows to the current market price.

Bond pricing relationship (inverse relationship):

• When interest rates rise, bond prices fall (YTM rises).
• When interest rates fall, bond prices rise (YTM falls). This is the fundamental rule of fixed income investing.

Yield types:

• Current Yield = Annual Coupon ÷ Market Price (ignores capital gain/loss)
• YTM = total return including price change (more accurate)
• Yield to Call (YTC) = YTM calculated to the call date instead of maturity

Worked example: Bond: $1,000 face value, 4% coupon ($40/year), 8 years to maturity, currently trading at $920. Approximate YTM = ($40 + ($1,000 − $920) ÷ 8) ÷ (($1,000 + $920) ÷ 2) = ($40 + $10) ÷ $960 = $50 ÷ $960 = 5.21% YTM

Because the bond trades at a discount ($920 against $1,000 face), the YTM of 5.21% comes out higher than the 4% coupon. The extra return is the $80 pull to par that the holder collects at maturity.

The book formula is an approximation, and it is a slightly low one. Solve the price equation properly and the same bond yields 5.25%. The gap is small at eight years and grows with maturity, which is why the calculator above runs the iterative solve rather than the shortcut. It shows you both so you can see the size of the error.