Carol is a professional tennis player ranked in the top 50 in the world.  She is currently 21 years old.  She will be able to play tennis until the age of 34.  After that she will coach the next generation of tennis stars.  

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

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

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

Carol has also been approached by Nikey, a large sports company that would like to use her in their advertisements.  She 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. 

She currently plans to save 20% of her earnings annually.  In year 5 when she signs the endorsement deal she 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%.  She 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.  

Disclaimer - the earnings provided in this question are not an accurate depiction of what a tennis player will earn at these levels. Carol will earn much more once she attains these rankings!

How much will she have saved at the end of her professional tennis playing career?