How do you calculate yield to maturity?

Solve Price = Σ C ÷ (1 + i)t + F ÷ (1 + i)n for i by trial and error or a numerical method, then multiply i by the number of coupons per year.

What is the YTM approximation formula?

YTM ≈ [annual coupon + (face − price) ÷ years] ÷ [(face + price) ÷ 2]. It is usually within a few hundredths of a percent.

Why is YTM different from the coupon rate?

The coupon rate is fixed on the face value; YTM reflects the price you pay. Buying below par raises the yield above the coupon rate.

Is YTM the same as the bond's return?

Only if you hold to maturity, receive every payment and reinvest coupons at the YTM.

Yield to Maturity (YTM) Formula

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Yield to Maturity (YTM) Calculator

Yield to maturity is the single discount rate that makes the present value of a bond’s remaining coupons and face value equal to its current price. It is the bond’s internal rate of return if you buy it today and hold it to maturity, assuming coupons are reinvested at the same yield, and it is the standard way bonds are quoted and compared.

Formula

Price = Σ_t=1ⁿ C(1 + i)^t + F(1 + i)ⁿ, solve for i; YTM = i × k Approximation: YTM ≈ C_a + (F − P) ÷ t(F + P) ÷ 2

Where

P: current bond price
C: coupon per period (C_a = annual coupon)
F: face value
i: yield per period
k: coupons per year
n: number of remaining coupons
t: years to maturity

Calculator

Bond price (P)

Face value (F)

Annual coupon rate (%)

Years to maturity

Coupons per year

Result and step-by-step solution

Yield to maturity

5.6617%

Quoted as an annual rate with semi-annual compounding (bond-equivalent yield). Effective annual yield 5.7418%; current yield 5.263%.

Per-period cash flows
C = 1,000.00 × 5% ÷ 2 = 25.00; n = 20
Starting estimate
YTM ≈ 50.00 + (1,000.00 − 950.00) ÷ 10(1,000.00 + 950.00) ÷ 2 = 5.641%
Solve the price equation exactly
Bisection finds the per-period yield i at which the present value of the cash flows equals 950.00: i = 0.02830845
Annualize
YTM = 0.02830845 × 2 = 5.6617%
Check
Price at this yield = 950.00 ✓

How to use the formula

There is no closed-form formula for YTM, so it is solved numerically. The calculator starts with the common approximation [C_a + (F − P) ÷ t] ÷ [(F + P) ÷ 2], then finds the exact per-period yield by bisection and multiplies by the number of coupons per year to give the annual yield in bond-equivalent form. It also shows the effective annual yield and checks the answer by repricing the bond.

A 10-year bond with a 5% semi-annual coupon priced at 950 has a YTM of 5.66%; the approximation gives 5.64%. Because the price is below par, YTM is above both the coupon rate and the current yield of 5.26%. To price a bond from a yield instead, use the bond price formula.

Frequently asked questions

How do you calculate yield to maturity?: Solve Price = Σ C ÷ (1 + i)^t + F ÷ (1 + i)ⁿ for i by trial and error or a numerical method, then multiply i by the number of coupons per year.
What is the YTM approximation formula?: YTM ≈ [annual coupon + (face − price) ÷ years] ÷ [(face + price) ÷ 2]. It is usually within a few hundredths of a percent.
Why is YTM different from the coupon rate?: The coupon rate is fixed on the face value; YTM reflects the price you pay. Buying below par raises the yield above the coupon rate.
Is YTM the same as the bond’s return?: Only if you hold to maturity, receive every payment and reinvest coupons at the YTM.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.