Question

8) How much should you be prepared to pay for a $1,000 10-year bond with an annual coupon of 6% and a yield to maturity of 7.5%?

Answer 1

Given,

Face value = $1000

Years to maturity (n) = 10 years

Annual coupon rate = 6%

Yield to maturity (r) = 7.5% or 0.075

Solution :-

Annual coupon payment (C) = $1000 x 6% = $60

Bond price

= C/r x [1 - (1 + r)^-n] + [face value x (1 + r)^-n]

= $60/0.075 x [1 - (1 + 0.075)^-10] + [$1000 x (1 + 0.075)^-10]

= $800 x [1 - (1.075)^-10] + [$1000 x (1.075)^-10]

= $800 x [1 - 0.4851939283] + [$1000 x 0.4851939283]

= $800 x 0.5148060717 + [$485.1939283]

= $411.84485736 + $485.1939283

= $897.04

You should be prepared to pay $897.04