Imagination Dragons Corporation needs to raise funds to finance a plant expansion, and it has decided to issue $30-$year zero coupon bonds with a par value of $$1,000$ each to raise the money. The required return on the bonds will be $8$ percent. Assume semiannual compounding periods.

a$.$ What will these bonds sell for at issuance? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ Using the IRS amortization rule, what interest deduction can the company take on these bonds in the first year? In the last year? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ Repeat part $($b$)$ using the straight$-$line method for the interest deduction. $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Issue price,$],[$b$.$ First year interest deduction,$],[$b$.$ Last year interest deduction,$],[$c$.$ Interest deduction,$]]$

d$.$ Based on your answers in $($b$)$ and $($c$),$ which interest deduction method would the company prefer?

IRS amortization rule

Straight$-$line method