Summarize the following:
To calculate the approximate yield to maturity, you need to know the coupon payment, the face value of the bond, the price paid for the bond and the number of years to maturity. These figures are plugged into the formula ApproxYTM=(C+((FP)/n))/(F+P)/2{\displaystyle ApproxYTM=(C+((F-P)/n))/(F+P)/2}. C = the coupon payment, or the amount paid in interest to the bond holder each year. F = the face value, or the full value of the bond. P = the price the investor paid for the bond. n = the number of years to maturity. Suppose you purchased a $1,000 for $920. The interest is 10 percent, and it will mature in 10 years. The coupon payment is $100 ($1,000x.10=$100{\displaystyle \$1,000x.10=\$100}). The face value is $1,000, and the price is $920. The number of years to maturity is 10. Use the formula: ($100+(($1,000$920)/10))/($1,000+$920)/2{\displaystyle (\$100+((\$1,000-\$920)/10))/(\$1,000+\$920)/2} Using this calculation, you arrive at an approximate yield to maturity of 11.25 percent. Plug the yield to maturity back into the formula to solve for P, the price. Chances are, you will not arrive at the same value. This is because this yield to maturity calculation is an estimate. Decide whether you are satisfied with the estimate or if you need more precise information. Use the formula P=C((1(1/(1+i)n))/i)+M/((1+i)n){\displaystyle P=C*((1-(1/(1+i)^{n}))/i)+M/((1+i)^{n})}, where, P = the bond price, C = the coupon payment, i = the yield to maturity rate, M = the face value and n = the total number of coupon payments. If you plug the 11.25 percent YTM into the formula to solve for P, the price, you get a price of $927.15. A lower yield to maturity will result in a higher bond price. The bond price you get when you plug the 11.25 percent interest figure back into the formula is too high, indicating that this YTM estimate may be somewhat low.
Gather the information. Calculate the approximate yield to maturity. Check the validity of your calculation.