Today is Carl's 24th birthday, and he wants to begin saving for retirement. To get started, his plan is to open an investment account, and to put $15,000 into the account today.

On Carl's 28'" birthday, and up to and including his 45th birthday, he will deposit $6,000 per year into his investment account.

When Carl is 45, he plans to deposit some equal annual amount of money, with the first deposit occurring on his 45th birthday, and the last occurring on his 65th birthday, as a way to ensure he has enough money necessary for his retirement withdrawals and charity donation.

Carl plans to retire at age 65 and he expects to live until age 90. Once he retires, Carl estimates that he will need to withdraw for living expenses $140,000 on his 65th birthday, with subsequent amounts increasing by 2% per year until his final withdrawal on his 89th birthday, these withdrawals will occur at the beginning of each year starting on his 65th birthday.

Carl would also like to donate $350,000 to his favourite charity when he is 70 years old.

Carl expects his investment account to earn 8% per year for the foreseeable future.

Given his plans, how much does he need to deposit each year starting on his 45th birthday and up to and including his 65th birthday, to ensure he has enough to cover his retirement withdrawals and donation?