Richard just graduated from college and wants to invest for his retirement. He will pay $5,000 into his retirement account now, then he will make payments of $100 into the account at the end of the month for the next ten years. Richard believes that after the first ten years he will be able to increase his payments to $300 each month for the next 20 years. After the 20 years, Richard plans to retire and begin to withdraw $2,000 from the account at the beginning of each month for 15 years, after which the account will be depleted. Richard believes that he will be able to earn 5.00% on his investment after the first ten years. What annual interest rate must he receive during the first ten years in order to receive for his plan to be successful?

Leslie is saving to purchase a Ferrari. She has no money to invest now, but will invest $3,200 each year for 15 years. By the end of the 15 years she will have her business established and will be able to make payments of $1,000 into the account each month. Finally she will let the money sit for ten years without making any payments and it will grow to $1,000,000, at which time Leslie can purchase the Ferrari of her dreams. Leslie's investment will earn 7.00%, monthly. How many payment of $1,000 must Leslie make in order for this plan to work?