Brian just graduated from engineering school and landed a sweet job earning $62000 per year. He expects his salary to increase by 4.9% per year. At the end of each year he will invest 10% of his salary into an investment account that earns 8.8.% per year compounded annually. He hopes to retire in 45 years. If all goes according to his plan, how much money will be in his retirement account when he retires? $  

After working for almost a year Brian decides he would rather spend Christmas in Mexico then put money in his retirement account. Each year he finds something else he wants to do with his retirement money until 15 years have passed and he realizes he has zero savings. Sure enough his salary increased by exactly what he had predicted over 15 years. He vows to start putting 10% of his salary away each year from then on. If all goes according to plan how much will be in his account after 30 more years when he reaches the age he would like to retire? $  

Brian is sad when he realizes how far he has fallen behind in his retirement planning. He decides to buy a lottery ticket hoping that he can use the winnings to put him back on track for his original retirement prediction. How much does he need to win and invest at the end of his 15th year working in order to get back to where he would have been if he had followed his original plan? $