QUESTION $3$

$($a$)$ Five years ago, AA Company issued $10,000($Ten Thousand$)20-$year, K$1,000$ par value bonds at par. At that time the market rate for such bonds was at $8\%.$ The coupon is paid annually. Today the actual market value of all the bonds together isK$11,942,450.$ What is the yield to maturity of these bonds today?

$(10$ marks$)$

$($b$)$ A bond that currently sells for $K1,167\mathrm{.}89$ has a par value of $K1,000$ and an annual coupon rate of $12\%.$ The bond makes semi$-$annual coupon payments and the appropriate discount rate for the bond $($i$.$e$.,$ the bond's yield to maturity$)$ is $10\%.$ How many years does this bond have remaining until it matures?

$(10$ marks$)$

What should be the price of a $K1,000$ par value, $10\%$ annual coupon rat $($coupon interest paid semi$-$annually$)$ bond with $10$ years remaining to maturi assuming a discount rate of $10\%?$

$(10$ marks$)$