1. Today is Dereks 25th birthday. Derek has been advised that he needs to have $2,194,277.00 in his retirement account the day he turns 65. He estimates his retirement account will pay 9.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 30.00th birthday and ending on his 65th birthday. How much must those deposits be?

2. Derek can deposit $11,000 on each birthday beginning with his 26th and ending with his 65th. What will the rate on the retirement account need to be for him to have $3,000,000 in it when he retires on his 65th birthday?

3. Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 72.0 when he fully retires, he will begin to make annual withdrawals of $177,251.00 from his retirement account until he turns 94.00. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 6.00% interest rate.