It depends on the bye-laws of the your society. You have said that there is nothing on this issue in the bye-laws. In that case, your society may have to take decision in this regard. Whatever decision is taken, should be made applicable to other similar cases too.
You can also check in your bye-laws, etc., whether there is a provision for waiver of interest amount on the late payment. This can also be kept in mind while taking decision, as mentioned above.
Generally speaking, it is not desirable to waive such interest on late payments, if there is a rule for charging interest on such late payments. The society / management can take a decision that the interest on late payment would not be waived and that part payment would not be adjusted against the interest on late payment. You can enforce such decision against the erring members and ask them to pay the full amount, i.e., the principle amount as well as the interest on the late payment.
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