On January $1,2024,$ Pebble held merchandise acquired from Rock for $\backslash (\backslash$$ $50,000\backslash ).$ During $2024,$ Rock sold merchandise to Pebble for $\backslash (\backslash$$ $120,000\backslash ),$ of which Pebble holds $\backslash (\backslash$$ $30,000\backslash )$ on December $31,2024.$ Rock's gross profit on sales is $\backslash (40\backslash \%\backslash ).$ On December $31,2024,$ Pebble still owes Rock $\backslash (\backslash$$ $5,000\backslash )$ for merchandise.

On December $31,2022,$ Pebble sold $\backslash$$$100,000$ par value of $\backslash (11\backslash \%,10\backslash )-$year bonds which resulted in an effective interest rate of $\backslash (10\backslash \%\backslash ).$ The bonds pay interest semi$-$annually on June $30$ and December $31.$ Both companies use the Effective Interest method to amortize any premium $/$ discount on the bonds.

On December $31,2023,$ Rock purchased $\backslash (\backslash$$ $50,000\backslash )$ par value of the parent's bonds, paying a price equal to par. The bonds are still held on December $31,2024.$

On December $31,2024,$ Pebble sold equipment with a cost of $\backslash (\backslash$$ $50,000\backslash )$ and accumulated depreciation of $\backslash (\backslash$$ $30,000\backslash )$ to Rock for $\backslash (\backslash$$ $40,000\backslash ).$ Rock will use the equipment beginning in $2025.$

On July $01,2024,$ the subsidiary signed a mortgage note with its parent for $\backslash (\backslash$$ $125,000\backslash ).$ Interest, at $\backslash (11\backslash \%\backslash )$ of the unpaid balance, and principal payments are due annually beginning July $1,2025.($For convenience, the mortgage balances are not divided into current and long$-$term portions.$)$

Pebble and Rock had the following trial balances on December $31,2024$:

Required:

$(1)$ Calculate the percentage interest of Rock Company's voting common stock that was acquired by Pebble Company on the date of acquisition.

$(2)$ Using TVM principles:

a$.$ Calculate how much Pebble Company received on December $31,2022$ for issuance of the bonds. Round up to the nearest dollar.

b$.$ State how much Rock Company paid to purchase $\backslash (50\backslash \%\backslash )$ of the bonds on December $31,2022.$

c$.$ Prepare the bond amortization schedule for the issuer of the bonds for the three$-$year period $2022$ to $2024.$ Round each figure to the nearest dollar.

$(3)$ Prepare the Eliminating and Adjusting Entries, the Schedules and Worksheet necessary to produce the consolidated financial statements of Pebble Company and its Rock for the year ended December $31,2024.$