Question

Union Local School District has bonds outstanding with a coupon rate of 3.8 percent paid semiannually and 29 years to maturity. The yield to maturity on these bonds is 2.9 percent and the bonds have a par value of $10,000.

What is the price of the bonds? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Price

$

Answer 1

Market value of bond = Present value of coupon payments + Present value of face value of bond

Semi-annual coupon payment = $10,000 * 3.8% * ½ = $190

Maturity of bond = 29 years

Number of semi-annual coupon payments = n = 29*2 = 58

Semi-annual yield to maturity = r = 2.9%/2 = 1.45% = 0.0145

Present value of annuity = Annuity amount*{1-(1+r)^-n}/r

Present value of semi-annual coupon payments = $190 * (1-1.0145^-58)/0.0145 = $7,417.98

Present value of face value of bond = $10,000/1.0145⁵⁸ = $4,388.91

Price of bond = $7,417.98 + $4,388.91 = $11,756.89