Question

what is the market price of a $300,000, ten - year, 5% bond issue sold to yield an effective rate of 3% if interest is paid semiannually?

a. $351,506

b. $242,087

c. $351,181

d. $353,437

please show calculations.

Answer 1

Semi annual interest payment = Par value of bonds x Stated interest rate x 6/12

= 300,000 x 5% x 6/12

= $7,500

Market interest rate = 3%

Semi annual Market interest rate = 1.5%

Maturity period of bonds = 10 years or 20 semi annual periods

Present value of principal to be received at the maturity = Par value of bonds x Present value factor (r%, n)

= 300,000 x Present value factor (1.5%, 20)

= 300,000 x 0.74247

= $222,741

Present value of interest to be paid periodically over the term of the bonds = Interest x Present value annuity factor (r%, n)

= 7,500 x Present value annuity factor (1.5%, 20)

= 7,500 x 17.16864

= $128,765

Market price of bond = Present value of principal to be paid at the maturity + Present value of interest to be paid periodically over the term of the bonds

= $222,741 + $128,765

= $351,506

Correct option is (a)