1. The force of interest per annum at time t, measured in years from the present,...

  

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1. The force of interest per annum at time t, measured in years from the present, is given by at 1+ at² 8(t) = for 0 ≤t≤8. The accumulated value of £20, 000 invested at time t=0 over 8 years' time is £43,266.62. (a) Obtain an expression for u(s, t), the accumulated value at time t of 1 at time s, in terms of a, s and t. [3] (b) Calculate the accumulated value at time t = 8 of payments of £5,000 at time t = 0 and £4,000 at time t = 5. [8] (c) Calculate the accumulated value at time t = 0 of a continuous payment stream paid between t = 2 and t = 7 at rate p(t) = 10,000√at²+1 per annum. [5] [16] 1. The force of interest per annum at time t, measured in years from the present, is given by at 1+ at² 8(t) = for 0 ≤t≤8. The accumulated value of £20, 000 invested at time t=0 over 8 years' time is £43,266.62. (a) Obtain an expression for u(s, t), the accumulated value at time t of 1 at time s, in terms of a, s and t. [3] (b) Calculate the accumulated value at time t = 8 of payments of £5,000 at time t = 0 and £4,000 at time t = 5. [8] (c) Calculate the accumulated value at time t = 0 of a continuous payment stream paid between t = 2 and t = 7 at rate p(t) = 10,000√at²+1 per annum. [5] [16]

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a To obtain an expression for us t the accumulated value at time t of 1 at time s we can use the for... View the full answer