You have been hired as the new controller for the Ralston Company. Shortly after joining the company in $2024,$ you discover the following errors related to the $2022$ and $2023$ financial statements:

a$.$ Inventory at $\frac{12}{31}\frac{?}{2022}$ was understated by $$7,800.$

b$.$ Inventory at $\frac{12}{31}\frac{?}{2023}$ was overstated by $$12,600.$

c$.$ On $\frac{12}{31}\frac{?}{2023},$ inventory was purchased for $$4,800.$ The company did not record the purchase until the inventory was paid for early in $2024.$ At that time, the purchase was recorded by a debit to purchases and a credit to cash.

The company uses a periodic inventory system.

Required:

Assuming that the errors were discovered after the $2023$ financial statements were issued, analyze the effect of the errors on $2023$ and $2022$ cost of goods sold, net income, and retained earnings. $($Ignore income taxes.$)$

Prepare a journal entry to correct the errors.