Question

​A bond with a 12 percent quarterly coupon rate has a yield to maturity of 16 percent. The bond has a par value of $1,000 and matures in 20 years. Based on this information, a fair price of this bond is $____.

Answer 1

fair value is $761

Step-by-step explanation:

Given data

bond value = $1000

rater r = 12 %

rate R = 16%

time = 20 year

to find out

a fair price

solution

we know compounding period in year is = 4

so time 20 x 4 = 80

fair Price =
`\sum_(k=1)^(k=80)` [(Quarterly Coupon) / (1 + R/400)^t] +bond value / (1 + R /400)^t

here

Quarterly Coupon = 12 × 1000/400 = 30

so

fair Price =
`\sum_(k=1)^(k=80)` [(30) / (1 + 16/400)^k] + 1000 / (1+16/400)^80

solve it we get

fair value is $761