What would be the initial offering price for the following bonds $($assume $$1,000$ par value and semiannual compounding$)?$ Do not round intermediate calculations. Round your answers to the nearest cent.

a$.$ A $15-$year zero$-$coupon bond with a yield to maturity $($YTM$)$ of $14\%.$

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b$.$ A $25-$year zero$-$coupon bond with a YTM of $10\%.$

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