You are making plans for your retirement. You have just turned 30 and want to retire on your 65th birthday. At that time, you plan to move to the Caribbean, where you believe you can live comfortably on $200,000 per year. You also understand that inflation can impact your enjoyment of retirement so you would like the annual payments you receive to increase at a rate of 5% per annum. Your first payment of $200,000 will occur at age 66. You intend to live in the Caribbean until your 85th birthday, when you will receive your last installment from your retirement fund, move back to Canada, and freeload off your kids. You would also like to save enough money so that you can buy a new car when you are 35, and pay for a big retirement party when you are 65. You figure you will need to have $35,000 for the car and $10,000 for the party.
You estimate that you can earn an average return of 10% per annum on any money you invest over the next 60 years. You have just begun working and plan on saving $11,000 per year until you are 35 years old. You will make your first deposit one year from now. To ensure that you are able to achieve your objectives, you must first answer the following problems: (15 marks)

a. How much will you have to accumulate before you retire?

b. How much will you have to save yearly, from your 36th to your 65th birthday, in order to accumulate the amount from part (a) and also pay for your retirement party?