PLEASE SHOW WORK 2. a. A $1,000 bond has a 7.5 percent coupon and matures after...
PLEASE SHOW WORK
2. a.
A $1,000 bond has a 7.5 percent coupon and matures after ten years.
If current interest rates are 10 percent, what should be the price
of the bond?
b. If after six years interest rates are still 10 percent, what
should be the price of the bond?
c. Even though interest rates did not change in a and b, why did
the price of the bond change?
d. Change the interest rate in a and b to 6 percent and rework your
answers. Even though the interest rate is 6 percent in both
calcula- tions, why are the bond prices different?
Homework Answers
| Price of bond | [Coupon amount*(1-((1+r)^-n)/r] + Face value*(1/(1+r^n) | |||||
| Coupon amount | 75 | 1000*7.5% | ||||
| a. | ||||||
| Calculation of price of bond today | ||||||
| Price of bond | 75*(1-(1.10^-10)/0.10)+1000*(1/(1.10^10)) | |||||
| Price of bond | (75*6.144567)+(1000*0.385543) | |||||
| Price of bond | $846.39 | |||||
| b. | ||||||
| Calculation of price of bond after six years | ||||||
| Price of bond | 75*(1-(1.10^-4)/0.10)+1000*(1/(1.10^4)) | |||||
| Price of bond | (75*3.169865)+(1000*0.683013) | |||||
| Price of bond | $920.75 | |||||
| c. | ||||||
| Though the interest rate of bond remains same, however as the bond reaches its maturity the price of bond would reach its par value and thus price of bond changes | ||||||
| d. | ||||||
| Calculation of price of bond today | ||||||
| Price of bond | 75*(1-(1.06^-10)/0.06)+1000*(1/(1.06^10)) | |||||
| Price of bond | (75*7.360087)+(1000*0.558395) | |||||
| Price of bond | $1,110.40 | |||||
| Calculation of price of bond after six years | ||||||
| Price of bond | 75*(1-(1.06^-4)/0.06)+1000*(1/(1.06^4)) | |||||
| Price of bond | (75*3.465106)+(1000*0.792094) | |||||
| Price of bond | $1,051.98 | |||||
| Though the interest rate of bond remains same, however as the bond reaches its maturity the price of bond would reach its par value and thus price of bond changes | ||||||
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