On $1/2/2024,$ Al$-$Andalus Industrial Company purchased equipment at a price of $200,000$ riyals. The purchase contract stipulated that the company pay $100,000$ riyals in cash upon purchase and pay the rest of the amount in $5$ equal annual payments, with the value of each installment being $20,000$ riyals. The first payment is due on $1/2/2024.5$ promissory notes were drawn from the company, each worth $20,000$ riyals, bearing no interest, noting that the interest rate for this type of operation is $12\%$ annually. The company made the payments on the agreed dates. Required:$1.$ Proof of the journal entry for the purchase of equipment$\mathrm{.}2.$ Proof of the journal entries for payment of the first, second, and third payments.