Final answer:
The false statement about the sale of an equity investment is that securities should remain on the balance sheet at amortized cost after sale.
Step-by-step explanation:
Out of the given options, the false statement about the sale of an equity investment is c. Securities should remain on the balance sheet at amortized cost after sale.
When an equity investment is sold, any gain or loss is recognized in the earnings at the time of sale, which contradicts option a. Additionally, a debit to cash is recorded for the sales proceeds, as stated in option b. However, securities should not remain on the balance sheet at amortized cost after sale. Instead, they should be removed from the balance sheet and any remaining cost should be recognized as a gain or loss on the income statement.
Therefore, option c is the false statement about the sale of an equity investment.