A $$1,000$ Treasury inflation$-$protected security is currently selling for $$965$ and carries a coupon interest rate of $3\mathrm{.}35$ percent.

a$.$ If you buy this bond, how much will you receive for your first interest payment, assuming no interest adjustment to principal during this time period?

b$.$ If there's a $0\mathrm{.}86$ percent increase in inflation, what will be the new par value of the bond?

c$.$ What is your new semiannual interest payment?

d$.$ What would the par value be at maturity, assuming a $3\mathrm{.}00$ percent annual inflation rate and ten$-$year maturity period? Click on the table icon to view the FVIF table $i.$

a$.$ If you buy this bond, assuming no interest adjustment to principal during this time period, your first interest payment would be $

$($Round to the nearest cent.$)$

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$\backslash$table$[[$Compound Sum of $$1($FVIF$)],[n,2\mathrm{.}00\%,2\mathrm{.}25\%,2\mathrm{.}50\%,2\mathrm{.}75\%,3\mathrm{.}00\%$