Question

5. Calculate the price of a 5 percent coupon bond with 12 years left to maturity and a market interest rate of 4 percent. (Assume interest payments are semiannual and par value is $1,000.) A. B. C. D. $971.33 $1,094.57 $1,191.20 $1,207.25

Answer 1

Price of a bond is mathematically represented as: 1 1 (1+ i)" P C i (1) where P is price of bond, with periodic coupon C, n periods to maturity, periodic YTM i and face value M.

M = $1000, n = 12 * 2 = 24 semi-annual periods, i = 4%/2 = 2% semi-annually, C = 5% * $1000/2 = $25 (semi-annually)

$P = 25 * \frac{1-\frac{1}{(1 + 0.02)^{24}}}{0.02} + \frac{1000}{(1 + 0.02)^{24}}$

P = $472.85 + $621.72

P = $1094.57 (Option B)