A bond trader purchased each of the following bonds at a yield to maturity of 7
ID: 2661071 • Letter: A
Question
A bond trader purchased each of the following bonds at a yield to maturity of 7 percent. Immediately after she purchased the bonds, interest rates increased to 7.5 percent. Which is the percentage change in the price of each bond after the increase in interest rates? Which bond is subject to the greatest interest risk rate? Assume a face value of $1,000 for all bonds.
a) 10 year, 9% semi annual coupon
b)30 year, 9% semi annual coupon
c) 5 year, 9% semi annual coupon
If you could please show me your work it would be really appreciated. Even if its how you imputed it into a finance caluclator
Explanation / Answer
A bond trader purchased each of the following bonds at a yield to maturity of 7 percent. Immediately after she purchased the bonds, interest rates increased to 7.5 percent. Which is the percentage change in the price of each bond after the increase in interest rates? Which bond is subject to the greatest interest risk rate? Assume a face value of $1,000 for all bonds.
At the time of Purchase , Bond Value
a) 10 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.5%,20,45,1000)
Bond Value = 1142.12
b)30 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.5%,60,45,1000)
Bond Value = 1249.45
c) 5 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.5%,10,45,1000)
Bond Value = 1083.17
After the interest rate rises , Bond Value
a) 10 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.75%,20,45,1000)
Bond Value = 1104.22
b)30 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.75%,60,45,1000)
Bond Value = 1178.03
c) 5 year, 9% semi annual coupon
Bond Value = pv (rate,nper,pmt,fv)
Bond Value = pv(3.75%,10,45,1000)
Bond Value = 1061.60
% Change in price
Which bond is subject to the greatest interest risk rate?
b)30 year, 9% semi annual coupon
At the time of Purchase After the interest rate rises Change in Price % Change in Price a) 10 year, 9% semi annual coupon 1,142.12 1,104.22 37.90 3.32% b)30 year, 9% semi annual coupon 1,249.45 1,178.03 71.41 5.72% c) 5 year, 9% semi annual coupon 1,083.17 1,061.60 21.57 1.99%
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