Yield at Maturity Formula
The yield to maturity is the annual return annual rate (discounted) earned over a bond kept until maturity. The yield to maturity is the discount rate estimated mathematically that equals the cash flow of payment of interest and principal received with the purchasing price of the bond.
This term is also referred to as internal rate of return or as the expected rate of return of the bond and it is the yield in which most bond investors are interested in.
The yieldto maturity is 8.5%. If you don’t have Microsoft Excel software on your computer, you can use the following approximation formula to determine the yieldtomaturity (YTM for the example:
YTM = Coupon payment + [ (1000  purchase price) / periods of maturity ] (1000 + purchase price) / 2
YTM = 50 + [ 1000 – 770.36) / 10 ] = 8.24%
( 1000 + 770.36) / 2
Using the approximation formula the 8.24% yield understates the true yieldtomaturity that is calculated using a computer. The reason is that the approximation formula does not use the time value of money for compounding of the coupon payments.
The yieldtomaturity depends on two assumptions:
 The bonds are held to maturity
 The interest payments received are reinvested at the same rate as the yieldtomaturity
If the bond is not kept until maturity, you could estimate the internal return rate of the bond by substituting the sales price of the bond for that of its maturity value and the period kept until the selling date for its maturity date.
The yieldtomaturity rate assumes that bondholders reinvest the received interests from the same yieldtomaturity. If this does not happen the owners return rate will differ from that of the quoted yieldtomaturity rate. For example, if the interest received is spent and not reinvested, the interest does not earn interest; the investor earns much lesser (or greater) rates, the 8% is not achieved. In reality matching the yieldtomaturity rate from the interest received is difficult because interest rates are changing constantly. The interest received is usually reinvested at different rates from the stated yieldtomaturity rate.
However, the yieldtomaturity is useful to compare and evaluate different bonds with variable qualities with different coupon rates and prices. For example when comparing the yieldtomaturity of an A&Arated bond with a BBBrated bond you can easily notice in how much would the yield increase when choosing the longerrated bond. Also you will observe the yield differential between bonds with different periods of maturity.
The relation between the coupon yield, current yield, yieldtomaturity, and the prices of the bonds are summarized next:
