4 Q3: Reinvestment (based on previous SoA FM question) Gurpreet deposits $8,000 into Fund X that pays monthly interest at a nom- inal annual rate i(12) = 2.4%. At the end of each year, Gurpreet withdraws all the interest earned in that year, plus $1,000 of the original investment (so Fund X is exhausted at the end of year 8), and deposits into Fund Y earning an effective annual rate of 1.75%. a) Prove that Gurpreet's deposits into Fund Y form an arithemtic annuity with initial deposit P and increment Q. Find P and Q. b) Calculate the amount of money in Fund Y at the end of 8 years