Question

You have just purchased a 10-year, $1,000 par value bond. The coupon rate on this bond is 6%, with interest being paid semi-annually. If you expect a 5% rate of return on this bond, how much did you pay for it? Show calculations.

Answer 1

price of the bond = (present value of annuity factor * coupon payments) + (present value factor * par value)

here,

present value of annuity = [1-(1+r)^(-n)]/r

here,

r =5% per year

=>5%*6/12 =>2.5% for 6 months.

n = 10 years*2 semi annual period => 20.

present value of annuity = [1-(1.025)^(-20)]/0.025

=>15.589164.

coupon payment =$1000*6%*6/12

=>$30.

present value factor =1/(1+r)^n

=>1/(1.025)^20

=>0.61027094.

face value =$1000.

=>[15.589164*30]+[1000*0.61027094]

=>467.67492+610.27094

=>$1,077.95