2. The force of interest 8 is a function of time and at any time t, measured in years, is given by the formula: 8(t) = 0.02 +0.0020 8(t) = 0.03 +0.005t Osts5 5 st s 10 a) Calculate the discount factor v(t) that applies for all t such that: 0 st s 10. [7 marks] b) Calculate the value at time t = 0 of 1,000 paid at time t = 8. [3 marks] [Total: 10 marks]