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

Answer:

Ans. Price of the bond is $9,250.57

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

$YTM(semi-annual)=(1+YTM)^{\frac{1}{2} } -1$

$YTM(semi-annual)=(1+0.056)^{\frac{1}{2} } -1=0.0276$

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

$Price=\frac{245((1+0.0276)^{39}-1) }{0.0276(1+0.0276)^{39} } +\frac{(245+10000)}{(1+0.0276)^{40} } =9250.57$

Best of luck.