The force of interest 8(t) at any time t, measured in years, is given by: (0.02 +0.003t² for 0 6 8(t) = 0.4-0.02t (i) Derive, and simplify as far as possible, expressions in terms of t for the present value of a unit investment made at time t. You should derive separate expressions for sub- intervals 0 < t ≤6 and t> 6. (ii) Hence, calculate the accumulated value at time t = 12 of £500 due for payment at time t = 4. (iii) Calculate the constant annual nominal rate of interest convertible quarterly implied by the transaction in part (ii).

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