Yield to maturity of a coupon bond

This yield to maturity calculator allows you to find yield to maturity of a coupon bond based on bond price, face value, coupon rate, coupon frequency, and years to maturity.

As you enter or change values, the calculator automatically updates and displays the yield to maturity.

Bond price($):

Face value ($):

Coupon rate (%):

Years to maturity:

Coupon frequency:

Yield to maturity: -

Related calculators:

YTM of a zero coupon bond Coupon bond price calculator Zero coupon bond price calculator

What is Yield to Maturity (YTM)?

Yield to Maturity (YTM) is a measure of the total return expected on a bond if it is held until maturity. It represents the bond’s internal rate of return (IRR), which equates the present value of its future cash flows (coupon payments and principal repayment) to its current market price. YTM takes into account the bond’s coupon payments, face value, market price, and time to maturity.

Formula for YTM

The general formula for YTM of a coupon bond doesn’t have a simple closed form, but it can be approximated through iterative methods (trial and error, Newton’s method, or a financial calculator). The theoretical relationship is expressed as follows:

P = \sum_{t=1}^{n} \frac{C}{(1+YTM)^t} + \frac{F}{(1+YTM)^n}

where:

$P$ = Present market price of the bond
$C$ = Annual coupon payment (Coupon rate * Face value)
$F$ = Face value of the bond (par value)
$YTM$ = Yield to maturity (what we solve for)
$n$ = Number of years to maturity

Since this equation doesn’t easily solve for YTM directly, it’s often calculated through approximation or using a financial calculator or software.

Approximate YTM formula

For a quick estimate, especially for small price differences, the following approximation can be used:

YTM \approx \frac{C + \frac{F - P}{n}}{\frac{F + P}{2}}

where:

$P$ = Present market price of the bond
$C$ = Annual coupon payment (Coupon rate * Face value)
$F$ = Face value of the bond (par value)
$n$ = Number of years to maturity

This approximation is useful for getting a rough idea of YTM without precise calculations.

Factors influencing YTM

Coupon rate: Higher coupon rates generally mean a higher YTM, assuming the bond price remains stable.
Time to maturity: Bonds with longer maturities tend to have higher interest rate risk, which affects YTM.
Market price: If a bond is selling at a discount (below face value), YTM is generally higher than the coupon rate; if selling at a premium, YTM is lower than the coupon rate.
Interest rate environment: As market interest rates rise, bond prices fall, which increases YTM.

Other key points about YTM

Relation to coupon rate: If a bond is purchased at par value, the YTM is equal to the coupon rate. If it’s purchased at a discount or premium, YTM adjusts accordingly.
YTM vs current yield: The current yield only considers the bond’s annual coupon payment divided by its price. It doesn’t account for the time value of money or capital gains/losses when the bond matures, unlike YTM.
YTM and interest rate risk: If interest rates rise, bond prices fall, leading to a higher YTM and vice versa.
Callable bonds: For bonds that can be called (redeemed early by the issuer), the yield to call (YTC) is also important to consider, as the bondholder might not receive payments up to maturity.