One year is 12 months, so during the first year, Kate spent $5/month * 12 months/year = $<<5*12=60>>60/year on the tickets.
After that, she went to the museum for 3 years - 1 year = <<3-1=2>>2 more years.
During this time, she visited the museum 2 years * 4 visits/year = <<2*4=8>>8 visits.
She had to pay the higher price of $7, so she spent $7/visit * 8 visits = $<<7*8=56>>56 in two last years.
In total Kate paid $56 + $60 = $<<56+60=116>>116 during 3 years.
#### 116