Have I correctly used 'date,' 'year's' and 'less' in my sentences?

Have I correctly used 'date,' 'year's' and 'less' in my sentences?

The actual date of the 87^th anniversary of the founding of Nelson's university was April 8, 2018. This year’s celebration, however, was held less than a week ahead of the actual date. (Context: The celebration was held on April 3, 2018.)