Arty is a professional skier ranked in the top 50 in the world. He is currently 21 years old.He will be able to ski until the age of 34.

Arty is a professional skier ranked in the top 50 in the world. He is currently 21 years old. He will be able to ski until the age of 34. After that He will coach the next generation of ski tennis stars. 

Given the short-term nature of a professional skiing career he realizes that he must save in order to achieve her future financial goals. 

Currently he earns $120,000 annually. He expects her earnings to grow at a rate of 3% throughout the 13 years. 

Based on his performance he is on track to be in the top 25 by year 5 and will have an increase in earnings by 35%. After that, he will be ranked #1 by year 8, which will generate an increase in his earnings by 50%. There will be no changes in her earnings once he reaches #1 and he will retire at the age of 34.

Arty has also been approached by Nikey, a large sports company that would like to use him in their advertisements. He will sign a deal with them in year 5 and will receive an annuity of $500,000 for a period of 3 years on top of her regular earnings.

He currently plans to save 20% of her earnings annually. In year 5 when he signs the endorsement deal he will increase her savings to 40% for the term of the contract and then drop back down to 20% for the last 5 years. 

Assume inflation is 2%. He earns 7.5% on her deposits (after-tax). Use real after-tax rates for your calculation. Assume all earnings noted throughout the question are after-tax. All payments are at the end of the year. 

How much will he have saved at the end of his professional skiing career?