Question

Union Local School District has bonds outstanding with a coupon rate of 4.9 percent paid semiannually and 20 years to maturity. The yield to maturity on these bonds is 5.6 percent and the bonds have a par value of $10,000. What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Ans. Price of the bond is $9,250.57

Step-by-step explanation:

Hi, first we need to establish the semi-annual coupon of the bond and the semi-annual discount rate (YTM semi-annually)

Coupon=10000*(4.9%/2)= $245

To turn the annaul YTM to semi-annual, we have to use the following equation

`YTM(semi-annual)=(1+YTM)^{(1)/(2) } -1`

`YTM(semi-annual)=(1+0.056)^{(1)/(2) } -1=0.0276`

After all this, we are ready to find the price, here is the math of this.

`Price=(245((1+0.0276)^(39)-1) )/(0.0276(1+0.0276)^(39) ) +((245+10000))/((1+0.0276)^(40) ) =9250.57`

Best of luck.