If the annuity for a widow of a present employee, or of a policeman in the police service of the city prior to but not on the day before the effective date, who re-entered service after that date and before age 57 is less than the amount of annuity specified in this section, the widow shall receive the following annuity after the present employee’s or policeman’s death: an amount equal to the sum produced by multiplying $30 by the number of years of service, not in excess of 20, including his last year of service but in no case less than 7 1/2% of his final salary.
     The annuity shall be paid to the widow of a present employee or policeman who (1) dies in service, or (2) withdraws and enters upon annuity, or (3) has served 20 or more years and withdraws before age 50 and dies before he enters upon annuity.