$27.1.$ A bond originally sold at par for $$1,000.$ The coupon rate on the bond is $9\%$ while the current discount rate for the bond is $10\%($APR$,$ compounded semi$-$annually$).$

a$.$ Assuming no change in risk, would this bond sell for more or less than its original issue price? Why?

b$.$ Given the current market rate of of $10\%($APR$.$ compounded semi$-$annuall$)$:

i$.$ Would a $$1000$ face value, $9\%$ coupon bond with $4$ years left to maturity and annual coupons be priced higher or lower than the $4-$year bond in $($a$)$ above? Why? There is no calculation required, just briefly state your argument.

ii$.$ Would a $$1000$ face value, $9\%$ coupon bond with $8$ years left to maturity and semi$-$annual coupons be priced higher or lower than the $4-$year bond in $($a$)$ above? Why? Again, there is no calculation required, just briefly state your argument.