Question $1.$ A zero$-$coupon bond pays no coupons and only pays a redemption amount at the time the bond matures. Isabella can buy a zero$-$coupon bond that will pay $12,000$ at the end of $12$ years and is currently selling for $6245\mathrm{.}78.$ Intead she purchases a $9\%$ bond with coupons payable that will pay $12,000$ at the end of $12$ years. If she pays X she will earn the same annual effective interest rate as the zero coupon bond $.$ Calculate X$.$

Question $2.$ Two bonds, each of face amount $200,$ are offered for sale at a combined price of $460.$ Both bonds have the same term to maturity but the coupon rate for one is twice that of the other. The difference in price of the two bonds is $50.$ Prices are based on a nominal annual yield rate of $2\mathrm{.}85\%.$ Find the coupon rates of the two bonds.

Question $3.$ Two $$1500$ bonds redeemable at par at the end of the same period are bought to yield $3\mathrm{.}5\%$ convertible semiannually. One bond costs $$1845\mathrm{.}72$ and has a coupon rate of $5\mathrm{.}25\%$ convertible semiannually. The other bond has a coupon rate of $3\mathrm{.}10\%$ payable semianually. Find the price of the second bond.

Question $4.$ A bond with face and redemption amount of $3000$ with annual coupons is selling at an effective annual yield rate equal to twice the annual coupon rate. The present value of the coupons is equal to the present value of the redemption amount. What is the selling price?

Question $5.$ A $$1500$ two$-$year $11\%$ bond, redeemable at par, with semiannual coupons, is bought at a premium to yield an $8\mathrm{.}2\%$ return, convertible semiannually. Construct an amortization schedule to show the amortization of the premium and the outstanding balances $($book values$)$ just after coupons are paid at the end of each half$-$year. Find the totals for the columns for the interest earned, payments, and principal repaid. $1$