Question 1 [4 marks) Yusuf has just graduated with his Hons in Actuarial Science with distinction. He comes from a financially challenging background and has just barely been able to pay his fees with the help from many different sponsors. With his excellent results he has just secured a well-paying job at one of the top consultancies in Sandton. In his gratitude to his sponsors, Yusuf would like to set up an education trust fund in their names as a legacy so that talented students who find themselves in the same situation are able to get assistance. He plans to contribute a portion of his income over the next 40 years of his career for this purpose. In exactly 40 years he wants the fund to pay out R300 000 per year payable semi- annually without an end date in mind to eligible top students. He would like to contribute a level amount X at the start of every month for the duration of his 40 year career. He knows he will be able to double his normal contribution every December when he receives his bonus. The interest rate will be 7% effective per annum for the first 25 years followed by a force of interest of 10% thereafter. Calculate the required monthly contribution X