Consider two bonds, a 3-year bond paying an annual coupon of 9%, and a 20-year b
ID: 2786249 • Letter: C
Question
Consider two bonds, a 3-year bond paying an annual coupon of 9%, and a 20-year bond, also with an annual coupon of 9%, Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity ofthe two bonds increases to 12%, a. What is the new price of the 3-year bond? (Round your answer to 2 decimal places.) Price of the 3-year bond b. What is the new price of the 20-year bond? (Round your answer to 2 decimal places.) Price of the 20-year bond c. Do longer or shorter maturity bonds appear to be more sensitive to changes in interest rates? Longer O ShorterExplanation / Answer
Price of 3 year bond
Price of the bond can be calculated using below formula
If,
Face value (F)= 1000
Interest rate [r]= 0.09
Years to maturity (n)= 3
YTM= 0.12
Annual coupon C= 90
Let's put all the values in the formula
Price of the bond= C[1- (1+ YTM)^-n/ YTM]]+ F/ (1+ YTM)^n
= 90[1- (1+ 0.12)^-3/ 0.12]+ 1000/ (1+ 0.12)^3
= 90[1- (1.12)-^3/ 0.12]+ 1000/ (1.12)^3
= 90[1- (0.711780247813411)/0.12]+ 1000/1.404928
= 90[0.288219752186589/ 0.12]+ 711.780247813411
= 90[2.40183126822158]+ 711.780247813411
= 216.164814139942+ 711.780247813411
= 927.945061953353
So price of the bond will be 927.95
Price of 20 year bond
Price of the bond can be calculated using below formula
If,
Face value (F)= 1000
Interest rate [r]= 0.09
Years to maturity (n)= 20
YTM= 0.12
Annual coupon C= 90
Let's put all the values in the formula
Price of the bond= C[1- (1+ YTM)^-n/ YTM]]+ F/ (1+ YTM)^n
= 90[1- (1+ 0.12)^-20/ 0.12]+ 1000/ (1+ 0.12)^20
= 90[1- (1.12)-^20/ 0.12]+ 1000/ (1.12)^20
= 90[1- (0.103666765080688)/0.12]+ 1000/9.64629309327495
= 90[0.896333234919312/ 0.12]+ 103.666765080688
= 90[7.4694436243276]+ 103.666765080688
= 672.249926189484+ 103.666765080688
= 775.916691270172
So price of the bond will be 775.92
More the maturity, more the price of the bond will be sensitive to interest rate changes
Price of the bond can be calculated using below formula
If,
Face value (F)= 1000
Interest rate [r]= 0.09
Years to maturity (n)= 3
YTM= 0.12
Annual coupon C= 90
Let's put all the values in the formula
Price of the bond= C[1- (1+ YTM)^-n/ YTM]]+ F/ (1+ YTM)^n
= 90[1- (1+ 0.12)^-3/ 0.12]+ 1000/ (1+ 0.12)^3
= 90[1- (1.12)-^3/ 0.12]+ 1000/ (1.12)^3
= 90[1- (0.711780247813411)/0.12]+ 1000/1.404928
= 90[0.288219752186589/ 0.12]+ 711.780247813411
= 90[2.40183126822158]+ 711.780247813411
= 216.164814139942+ 711.780247813411
= 927.945061953353
So price of the bond will be 927.95