IBM issued a thirty year, $$45,000,000$ bond issue on February ${16}^{th},2015.$ The bonds had a $9\%$ coupon rate and paid interest semiannually on February ${15}^{th}$ and August ${15}^{th}.$ At the time of issuance the market rate of interest was $10\%($compounded semiannually$).$

Determine the following:

a$.$ The price for which a $$1,000$ face value bond sold on the issue date.

b$.$ The price at which a $$1,000$ bond would be selling on February ${16}^{th},2024,$ if the market rate of interest had remained at $10\%.$

c$.$ The holding$-$period yield $($expressed as an APR$)$ a bondholder would have earned by purchasing the bond on the issue date and selling it on February ${16}^{th},2024($ignore transactions costs and taxes$).$ The holding$-$period yield can be viewed as the achieved Internal Rate of Return $($IRR$).$