The yield to maturity formula, also known as book yield or redemption yield, is used in finance to calculate the yield of a bond at the current market price. It is calculated to compare the attractiveness of investing in a bond with other investment opportunities.

YTM (Yield to Maturity) is the annual income level or profitability, which investors gain by buying a bond or other fixed-interest security at the current market price and holding it in their portfolio until maturity. The Yield to Maturity of a bond is the discount rate at which the current price of the bond is equal to the sum of all the future Cash Flows from the investment into the bond.

YTM or the Book Yield is often compared to the internal rate of return (IRR) of investing in bonds. It is interpreted as the rate that the investor earns by investing in the bond that he bought at the current price and held it until maturity, reinvesting the received interest based on that rate of return.

Yield to Maturity can be used to determine whether to make an investment into a bond. After calculating the YTM an investor compares it to his or her required yield and decides if it’s a good investment. Because YTM is an annual rate, the investor can also compare bonds with different coupons and maturities.

### How to Calculate Yield to Maturity?

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

Where P = current price, C = coupon/interest payment, F = face/maturity value, and n = the number of years to maturity.

Calculations of Yield to Maturity (YTM) assume that the bond is held to maturity, coupon payments are reinvested at the same rate as the bond’s current yield and all the payments are made on time.

### Difference between YTM and the Coupon Rate

A coupon rate is an interest paid to the bondholder who receives it every year from the bond’s issue date until it matures.

• YTM > Coupon Rate

The current YTM rate is higher than the bond coupon rate ⇒ the bond is selling at a discount. The difference between the nominal value and the market value of the bond = discount.

• YTM < Coupon Rate

The current YTM rate is lower than the bond coupon rate ⇒ the bond is selling at a premium. The difference between the nominal value and the market value of the bond is a premium.

• YTM = Coupon Rate

The current YTM rate is equal to the bond coupon rate ⇒ the bond is selling at par. The current price of the bond is equal to its nominal value.

There are also zero-coupon bonds.  A zero-coupon bond is a type of bond, where there are no coupon payments. At the time of maturity, the bondholder receives the face value of the bond, which means that the current price has to be lower than the face price. The investor’s earnings come entirely from the gain on redemption.

Yield to Maturity for zero-coupon bonds is calculated as:

$YTM = \bigg(\frac{F}{PV}\bigg)^{\frac{1}{n}} - 1$

Where F = face value, PV = present value, and n = the number of periods.

Face Value is a bond’s maturity value, or, in other words, the amount of money paid to the holder at the maturity date. For U.S. government bonds it’s usually $1000, for U.K. Gilts it’s £100. ### Examples of Yield to Maturity formula Example 1. Assume you want to buy a bond and want to evaluate what YTM of this bond would be. • The Face Value of the bond is £100. • The Price of a bond is £93.50. • Annual Coupon Rate is 7%. • There are 10 years until the maturity. $YTM = \frac{\£7 + \frac{\£100-\£93.50}{10}}{\frac{\£100 + \£93.50}{2}} = 7.9\%$ The expected yield to maturity is 7.9% annually. Example 2. Assume you want to buy a zero-coupon bond and want to evaluate what YTM of this bond would be. • The Face Value of the bond is$1,000.
• The Price of the bond is \$865.
• There are 2 years until the maturity.
$YTM = \bigg(\frac{\1,000}{\865}\bigg)^{\frac{1}{2}} - 1 = 7.52\%$

The yield to maturity of this zero-coupon bond is 7.52%.