Question
In: Finance
You buy a 30-year zero coupon bond with a face value of $1000 and a 4%...
You buy a 30-year zero coupon bond with a face value of $1000 and a 4% interest rate, compounded semi-annually. The moment after you buy the bond, the interest rate falls to 3%, compounded semi-annually. What is the percent change in the bond price? Note: the sign is important!
Solutions
Expert Solution
| Par/Face value | 1000 | ||||||||||||||
| Annual Coupon rate | 0 | ||||||||||||||
| Annual coupon | 0 | ||||||||||||||
| semi-annual coupon | 0 | ||||||||||||||
| Present Value = Future value/[(1+(r/m))^mt] | |||||||||||||||
| r is the interest rate that is 4%. | |||||||||||||||
| m is the compounding period that is 2 | |||||||||||||||
| mt is the time period. | |||||||||||||||
| price of the bond = sum of present values of future cash flows | |||||||||||||||
| r/2 | 0.02 | ||||||||||||||
| mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 60 |
| future cash flow | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1000 |
| present value | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 304.7823 |
| sum of present values | 304.78 | ||||||||||||||
| The price of the bond when the interest rate is 4% is $304.78. | |||||||||||||||
| Par/Face value | 1000 | ||||||||||||||
| Annual Coupon rate | 0 | ||||||||||||||
| Annual coupon | 0 | ||||||||||||||
| semi-annual coupon | 0 | ||||||||||||||
| Present Value = Future value/[(1+(r/m))^mt] | |||||||||||||||
| r is the interest rate that is 3%. | |||||||||||||||
| m is the compounding period that is 2 | |||||||||||||||
| mt is the time period. | |||||||||||||||
| price of the bond = sum of present values of future cash flows | |||||||||||||||
| r/2 | 0.015 | ||||||||||||||
| mt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 60 |
| future cash flow | 0 | 0 |
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