A city that levied the tax authorized by this act before the effective date of this section may amend the ordinance to increase the rate to an annual tax of not more than 1.4% on corporations and resident individuals and not more than 0.7% on nonresident individuals. The increase in the tax authorized by this section shall be levied for not longer than 13 years as provided in the ballot proposal submitted to the electors. An amendment to the city income tax ordinance under this section is not effective unless the amendment is approved before July 1, 1988 by a majority vote of the registered and qualified electors of that city voting on the proposition. This section applies only to a city that has a population of more than 50,000 and that, within 6 years before the approval of the amendment authorized by this section, annexes to the city an area containing more than 20 square miles.