The estate or designated beneficiary of any permanent policeman who shall die after having retired under the provisions of N.H. Rev. Stat. § 103:14 or 15 shall be entitled to receive from the retirement fund any excess of the total payments made thereto by him, without interest, over the aggregate retirement allowance payments received by him prior to his death. In addition, a lump sum equal to $3,600 shall be payable, except in the case of a former policeman who was employed by a city having a population of more than 34,000 inhabitants, in which case the lump sum shall not exceed the amount of the assessed part of his annual salary at retirement.