If i exercise 45mins a day at heart rate 140-160bpm. how much fitter will i be in 3 months and then 6 months?

Daily exercise: Most emphasis in todays hectic high paced lifestyles is intense workouts for short periods of time. The so called 4 minute, this and 4 minute that. Intense quick shots are producing good results. Given your age and duration of time you are maintaining that cardiac level, as long as all else is good with your health, and you are judicious with what you do between workouts i would expect very fit.

More fit likely: I do not know a measure, except doing the same effort with less increase in pulse rate. Longer duration, and less tiredness and breathlessness.

Many benefits : Exercise, depending on its type, has many benefits to your body and mind. The type most beneficial to your heart is 30-40 minutes a day of moderate intensity cardio exercise ( where you get short of breath and your heart rate is higher, like running or treadmill, or elliptical). 5 times a week of this should be your target. It will have profound benefits over your lifetime.