Starting a year from now and making 10 yearly payments, Pierre would like to put into a retirement account enough money so that, starting 11 years from now, he can withdraw $30000 per year until he dies. Pierre is confident that he can earn 8% per year on his money for the next 10 years, but he is only assuming that he will be able to get 5% per year after that. 

a) How much does Pierre need to pay each year for the first 10 years in order to make the planned withdraw? 

b) Pierre's will states that, upon his death, any money left in his retirement account is to be donated to the Princeton Mathematics Department. If he dies immediately after receiving his 17th payment, how much will the Princeton Mathematics Department inherit?