Which of the following bonds has the largest percentage change in price when the market interest rate decreases from $8\%$ to $7\%?$

a$.$ A $10-$year bond with $10\%$ annual coupon with $$1000$ face value

b$.$ A $5-$year zero with $$1000$ face value

c$.$ A $10-$year zero with $$1000$ face value

a$.$ A $30-$year zero with $$100$ face value

Solution

$\backslash$table$[[,$Price at $8\%,$Price at $7\%,$Pctge. change$],[10-$year, $10\%$ annual coupon,$$1,134\mathrm{.}20,$$$1,210\mathrm{.}71,6\mathrm{.}75],[10-$year zero,$463\mathrm{.}19,508\mathrm{.}35,9\mathrm{.}75],[5-$year zero,$680\mathrm{.}58,712\mathrm{.}99,4\mathrm{.}76],[30-$year zero,$99\mathrm{.}38,131\mathrm{.}37,32\mathrm{.}19]]$ Please show step by step how to slove