Calculating the yield to maturity

The yield to maturity (YTM) measures the interest rate, as implied by the bond, that takes into account the present value of all the future coupon payments and the principal. It is assumed that bond holders can invest received coupons at the YTM rate until the maturity of the bond; according to risk-neutral expectations, the payments received should be the same as the price paid for the bond.

Let's take a look at an example of a 5.75 percent bond that will mature in 1.5 years with a par value of 100. The price of the bond is $95.0428 and coupons are paid semi-annually. The pricing equation can be stated as follows:

Here, is the coupon dollar amount paid at each time period, is the time period of payment in years, is the coupon payment frequency, and is the YTM that we are interested to solve. To solve for YTM is typically a complex process, and most bond YTM calculators use Newton's method as an iterative process.

The bond YTM calculator is illustrated...