A newly issued $20-$year maturity, zero$-$coupon bond is issued with a yield to maturity of $9\mathrm{.}0\%$ and

face value $$1,000.$ Find the imputed interest income in $($a$)$ the first year; $($b$)$ the second year; and $($c$)$

the last year of the bond's life. Assume annual coupon payments.

Note: Round your answers to $2$ decimal places.