Question

Assume a 10-year $1,000,000 bond issued with a 2.5% annual contractual rate, but with a current market interest rate of 1.5%.

a) Determine the selling price of the bond.

b) Determine the amount of the premium.

Answer 1

a)

Annual interest payment = Par value of bonds x Stated interest rate

= 1,000,000 x 2.5%

= $25,000

Market interest rate = 1.5%

Maturity period of bonds = 10 years

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

= 1,000,000 x Present value factor (1.5%, 10)

= 1,000,000 x 0.86167

= $861,670

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

= 25,000 x Present value annuity factor (1.5%, 10)

= 25,000 x 9.22218

= $230,555

selling price of the 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

= $861,670 + $230,555

= $1,092,225

b)

Amount of the premium = selling price of the bond - Par value of bonds

= 1,092,225 - 1,000,000

= $92,225