7. You will pay into a pension fund until you are aged 65. You are expected to live until your 80th birthday. You are currently 21 years of age. Pension fund contributions are made bi-weekly (use n=2/52) beginning in 2 weeks time. If you are promised an interest rate of 7% compounded monthly:

i) What should be the size of your contribution if you plan to have $1 million at age65?

ii) Following your final contribution at age 65, you will retire. You will begin to withdraw money at the end of each month at a declining rate. Each subsequent withdrawal will fall by a constant rate of 0.5% per month for the duration of your life. You withdraw the final payment an instant before you die. If the effective annual rate of interest that you can receive on your pension fund is 5% what is the most that you can withdraw on your first payment?

iii) If your contribution is $100.00 bi-weekly, what is the future value of your pension fund immediately after the last payment if the prevailing interest rate remains 7% compounded monthly?

iv) If you wish to withdraw $5000 at the beginning of each month from the moment you retire until your 80th birthday , what is the effective annual interest rate that you require on your pension fund?