A $1,000$ Bond with coupon rate r convertible semi$-$annually will be redeemed at par in K years.

Purchase price to yield $10\%$ convertible semi$-$annually is P$.$

If coupon rate were r $0\mathrm{.}04,$ the price of the bond would be P $200.$

Determine the present value of a $3$K year annuity immediate with semi$-$annual payments of $100$ at a yield rate of $10\%$ convertible semi$-$annual.