I want to retire in 40 years. When I retire, I want to withdraw $20,000 every 6 months from my savings for a period of 10 years. However, at the end of years two and three in my retirement, I will need to spend $40,000 and $60,000 respectively to send my grandson to culinary school. Assuming I can earn 4% compounded semi-annually, answer the following question:

How much money will I need to deposit semi-annually over the next 40 years to achieve my retirement goals? The retirement goals include both semi-annual withdrawals and two cash flows associated with paying for culinary school.