You buy a bond for $979 that has a coupon rate of 7.6% and a 6-year maturity. A
ID: 2773303 • Letter: Y
Question
You buy a bond for $979 that has a coupon rate of 7.6% and a 6-year maturity. A year later, the bond price is $1,144. (Assume a face value of $1,000 and annual coupon payments)
What is the new yield to maturity on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
What is your rate of return over the year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
a.What is the new yield to maturity on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Explanation / Answer
a) After 1 year,
Price of the bond = $1,144
Time to maturity = 5 years
Annual Coupon = 7.6% * 1000 = $76
YTM or Yield to Maturity is the discount rate at which the discounted future cash flows are equal to the bond price.
Thus,
1144 = 76/(1+YTM)1+ 76/(1+YTM)2+ 76/(1+YTM)3+ 76/(1+YTM)4+ 1076/(1+YTM)5
Solving the above equation,
YTM = 4.33%
b) Rate at which the bond was bought (Cost Price of the Bond) = $979
Price of the bond after 1 year = $1,144
Coupon Earned During the Year = 7.6% * 1000 = $76
Gain from the Bond = Coupon + New Price - Cost Price = 1144 = 76 - 979 = $241
Rate of Return over the year = [{(Coupon + New Price) - Cost Price} / Cost Price] * 100
= [{(1144 + 76) - 979} / 979] * 100
= [(1220 - 979) / 979] * 100
= (241 / 979) * 100 = 24.62%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.