A company expects to receive the following payments from a customer: . 10,000 on 1.4.2017 4,500 on 1.7.2018 3,200 on 1.1.2022 The current date is 1 July 2016. This date represents t = 0, and hence 1 July 2017 represents t = 1. Assume that the discount function v(t) runs from time 0 to time t and is given by: 1 v(t) = 1-t2 60 (a) Find the value of each payment as at 1 January 2020. (5 marks] (b) Using the results from (a), or otherwise, find the value of all payments at 1 July 2023. [2 marks] Let p(t) represent a continuous payment of 200 per unit time. This is paid between t = 1 and t = 4. Now let 8(s) be the force of interest and is represented by: 8() = 0.1 + Bs (c) Write down an integral that represents the accumulated value at t = b (where b > 4) for this continuous payment. You should define all the elements of the integral. [3 marks] [Total: 10 marks]