2. (Annuities) (a) (2 marks) Compute the present value of an annuity due that pays 2,000 annually, at a rate of 3% p.a. effective, for 20 years. (b) (3 marks) Compute the accumulated value of an annuity immediate that makes semi-annual payments of 500 for 10 years and then it makes annual payments of 1,000 for another 10 years. The annual effective rate is 4%. (c) (3 marks) The annual effective rate is 5%. An annuity is paid continuously at a rate of P pounds per month. Its accumulated value after 10 years is 10,000. Find the monthly payment rate