Yield to Maturity (YTM)
Total annualised return if held to maturity
What is Yield to Maturity (YTM)?
Yield to Maturity (YTM) is the total annualised return an investor earns if they buy a bond today at the current market price, receive all coupon payments, and hold it until the bond matures at par value. YTM accounts for the current price (which may be above or below par), all future coupon cash flows, and the return of principal at maturity. It is the single most important yield measure for bonds and is used for all bond comparisons and valuation. When a bond trades at a discount (below par), YTM > coupon rate. At a premium (above par), YTM < coupon rate. YTM is solved numerically: there is no closed-form algebraic solution.
Formula
Price = Σ [C / (1+YTM)^t] + F / (1+YTM)^n
Solve for YTM by Newton-Raphson iteration
C = annual coupon payment (Face Value × Coupon Rate / n)
F = face/par value (typically $1,000)
n = years to maturity
t = each coupon period
Calculator
How to Use
- 1Enter bond details: Face value, annual coupon rate, years to maturity, and current market price.
- 2Solver finds YTM: The calculator iterates to find the discount rate that makes the present value of all cash flows equal the current price.
- 3Compare to coupon rate: If YTM > coupon rate, bond trades at discount. If YTM < coupon rate, bond trades at premium.
- 4Use for comparison: Compare YTM across bonds of similar credit rating and maturity to find relative value.
Worked Example
Example: Corporate bond at a discount
Face Value
$1,000
Coupon
5%
Price
$950
Years
10
A 5% coupon bond priced at $950 (discount) has YTM ≈ 5.61%. The extra 0.61% above the coupon rate comes from the $50 capital gain at maturity (buying at $950, receiving $1,000). The YTM blends this capital appreciation with the coupon income into a single annualised return figure.