Question

What would be the price of a $1,000,000 bond that matures in 20 years and has a stated rate (pays) of 10%: if the yield rate on the day of sale is 11%? please show steps

Answer 1

Assume annual compounding and annual payment of interest.

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

M = $1,000,000, n = 20, i = 11%, C = 10% * $1,000,000 = $100,000

$P = 100,000 * \frac{1-\frac{1}{(1 + 0.11)^{20}}}{0.11} + \frac{1,000,000}{(1 + 0.11)^{20}}$

P = $796,332.81 + $124,033.91

P = $920,366.72