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 Principal

Term of debt

Payment Interval

Interest Rate on Debt

Interest Rate on Fund

Conversion Period

Book Value Required After

$$$$18$ comma $00018,000$

$55$ years

$3$ months$3$ months

$88\%$

$7\mathrm{.}57\mathrm{.}5\%$

quarterlyquarterly

$22$ years