Lisa Carr purchased a newly$-$issued $25-$year bond that pays semi$-$annual coupons at an $8\%($annual$)$ rate. The bond has a par value $($and a redemption value$)$ of $1,000.$ The bond is callable on or after its $10$ th anniversary with a $10\%$ call premium $($i$.$e$.,1,100$ is payable if it is called$).$

Lisa purchased this bond at issue at a price that will assure her a rate of return of at least $7\mathrm{.}5\%($a nominal rate, convertible semi$-$annually$).$ If the bond is called on its ${12}^{th}$ anniversary, what is Lisa's actual rate of return?

$)7\mathrm{.}5\%$

$)7\mathrm{.}6\%$

C$)7\mathrm{.}7\%$

D$)7\mathrm{.}8\%$

E$)7\mathrm{.}9\%$

Suppose you enter into a $3-$quarter interest rate swap with a level notional amount as the receiver. The swap rate is based on the following zero$-$coupon bond prices:

$\backslash$table$[[$Bond term $($in quarters$),1,2,3,4],[\backslash$table$[[$Zero$-$coupon bond$],[$price per $100$ face$]],98\mathrm{.}40,96\mathrm{.}90,95\mathrm{.}30,93\mathrm{.}50]]$

What net interest rate will you pay in the second quarter if the spot interest rate for the second quarter is $0\mathrm{.}018?$

A$)0\mathrm{.}0010$

B$)0\mathrm{.}0012$

C$)0\mathrm{.}0016$

D$)0\mathrm{.}0018$

E$)$ a different rate

$31.$ The following table gives the term structure of spot interest rates.