= Problem 1 (12 marks) (Here, t = 0 is taken as current time) An investment fund is launched at time 0 and it earns interest at a force of interest 8t where (0.01 + 0.02t if t 2' where c is a constant. Question (a) Calculate the effective interest rate of the investment fund over the period [1,4]. (b) An investor deposits $15000 into this investment fund at time 0. Later, he deposits $4000 at time 2 and withdraw $3000 at time 3.5. Find the total amount of interest earned by the investor over the period (1,3). = Problem 1 (12 marks) (Here, t = 0 is taken as current time) An investment fund is launched at time 0 and it earns interest at a force of interest 8t where (0.01 + 0.02t if t 2' where c is a constant. Question (a) Calculate the effective interest rate of the investment fund over the period [1,4]. (b) An investor deposits $15000 into this investment fund at time 0. Later, he deposits $4000 at time 2 and withdraw $3000 at time 3.5. Find the total amount of interest earned by the investor over the period (1,3)