The debt in the table below is retired by the sinking fund method. Interest payments on the debt are made at the end of each payment interval and the payments into the sinking fund are made at the same time. Determine the following:$($a$)$ the size of the periodic interest expense of the debt;$($b$)$ the size of the periodic payment into the sinking fund;$($c$)$ the periodic cost of the debt;$($d$)$ the book value of the debt at the time indicated.Debt PrincipalTerm of debtPayment IntervalInterest Rate on DebtInterest Rate on FundConversion PeriodBook Value Required After$$43$ comma $00013$ years$6$ months$8\%9\%$semi dash annually$9$ yearsQuestion content area bottomPart $1($a$)$ The size of the periodic interest expense is $$1720.($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$Part $2($b$)$ The size of the periodic payment is $$1810\mathrm{.}59.($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$