Calculate a percentage increase that doesn't exceed 100%

Hello everyone,

I am currently working on an occupancy rate up model. Here is the scenario

I have a hotel with occupancy rate of 70% and ramp up 6 months 

I need to calculate the EOM occupancy rate and average occupancy rate 

EOM occupancy rate = 70%/6 = 0..7/6 = 0.1167 = 11.67%

while the average rate = (previous EOM occupancy rate + current EOM occupancy rate)/2 

For a 10 year plan, with the above function, the values will exceed 100% and in reality an hotel won't have 150% occupancy rate. 

I need to modify the function so that when EOM occupancy rate reaches 95%, it remains there. It won't exceed 100% even the plan is 100 years. Thank you