It depends on the employer's discretion and circumstances. The employee may be willing to pay the amount in lieu of notice period, but the duties and work involved may be timebound and the employer may find it difficult to recruit a fresher and complete the task within the time frame. Some tasks are such that only that employee can complete within that time frame as he is well acquainted with that task.
Members can only give guidance to that simple query and may not be interested in arguments that are not relevant.
It is proper for an employee to complete his tasks, earn goodwill and resign the institution with good relations.
As the employee is having such issues, employers may be having several issues and still, they are not having any forum, no one is going to shed even a tear to an employer who risks his amount, personal relations, family life, peace of mind and all for starting and running an institution.
It is difficult to find employees with Hanuman spirit that completes the task without any questions and not seeing his personal benefits/advantages.
Just focus on peace of mind and complete the task as it is just one month and you have been employed by the organization for some time and repay at least a fraction without expecting anything.
It may appear to you like a sermon, but once you become an employer you will be knowing their problems.