A company issued bonds for $$850,000$ and established a sinking fund to retire the debt in $15$ years. It made deposits at the end of every $6$ months into the fund and the fund was earning $3\mathrm{.}55\%$ compounded semi$-$annually.

a$.$ Calculate the size of the periodic sinking fund deposit.

b$.$ Calculate the sinking fund balance at the end of the ${11}^{th}$ payment period.

c$.$ Calculate the interest earned in the ${12}^{th}$ payment period.

d$.$ Calculate the amount by which the sinking fund increased in the ${12}^{th}$ payment period.

e$.$ Construct a partial sinking fund schedule to illustrate details of the last two payments. $($need help with steps for excel!$)$