A sentence is given with an underlined part that may need improvement. Choose the alternative that best improves the underlined part. In case no improvement is needed, select the option indicating No improvement. Sentence: Do you mind me leaving this payment until next year?

Introduction / Context:
This sentence improvement question focuses on a subtle point of grammar involving gerunds and possessive forms. In English, when a verb in its ing form functions as a noun, it can be preceded by a possessive adjective such as my, your, or his. Exam questions often check whether candidates recognise this pattern in polite expressions like Do you mind my coming in or Do you mind his smoking here.

Given Data / Assumptions:
The sentence given is Do you mind me leaving this payment until next year. The underlined word is me, and the options for replacement are I, my, mine, and No improvement. The context is a polite question asking for permission or checking if someone objects to a delay in payment. We assume standard formal or semi formal usage suitable for competitive exam standards.

Concept / Approach:
In constructions like Do you mind my leaving, the word leaving is a gerund, functioning as a noun phrase meaning the act of leaving. English grammar traditionally prefers a possessive form before the gerund when the person performing the action is mentioned. Therefore, my leaving this payment until next year is more grammatically correct and more polished than me leaving this payment in formal contexts. Among the given options, my is the possessive adjective that fits this rule.

Step-by-Step Solution:
Step 1: Identify leaving as a gerund, which acts like a noun describing an action. Step 2: Recognise that the pronoun before a gerund is often in the possessive form in careful written English. Step 3: Replace me with each option and read the sentence: Do you mind I leaving, Do you mind my leaving, Do you mind mine leaving, and the original Do you mind me leaving. Step 4: Notice that my leaving sounds natural and grammatically correct, while I leaving and mine leaving are clearly wrong. Step 5: Conclude that my is the correct replacement for me in this formal exam style sentence.

Verification / Alternative check:
To verify the rule, consider similar sentences such as Would you mind my opening the window or Do you mind his calling so late. In each case, the possessive form is preferred before the ing form that acts as a noun. Modern spoken English often uses object pronouns like me or him, but competitive exams usually test the more formal possessive pattern. Therefore, replacing me with my in the question sentence aligns with the rule they wish to examine.

Why Other Options Are Wrong:
I is a subject pronoun and cannot directly precede a gerund in this structure, so Do you mind I leaving is grammatically incorrect.
Mine is a possessive pronoun used without a following noun, as in This book is mine, and cannot correctly stand before leaving in this sentence.
No improvement cannot be accepted because the exam expects the formal structure with a possessive before the gerund and therefore treats me leaving as non standard usage in this context.

Common Pitfalls:
In everyday conversation, many speakers say Do you mind me coming instead of Do you mind my coming, which can make the exam version seem unfamiliar. Candidates must remember that competitive exams often favour traditional grammar rules. Recognising patterns like someone minding my doing something or his doing something can help secure marks in sentence improvement questions that focus on subtle but important points of usage.

Final Answer:
The underlined word should be improved to my, so the sentence reads Do you mind my leaving this payment until next year.