Sepia Inc. issued bonds for $$325,000$ that were redeemable in $9$ years. They established a sinking fund that was earning $4\mathrm{.}87\%$ compounded semi$-$annually to pay back the principal of the bonds on maturity. Deposits were being made to the fund at the end of every $6$ months.

Calculate the size of the periodic sinking fund deposit.

Calculate the sinking fund balance at the end of the payment period $12.$

Calculate the interest earned in payment period $13.$

Calculate the amount by which the sinking fund increased in payment period $13.$