* The force of interest 8(t) at time t (measured in years) is a +bt² where a and b are constants. An amount of £200 at time t = 0 accumulates to £210 at t = 5 and £230 at t = 10. (a) Show that a = b= log (1.05)-log(1.15) = 0.008352, 250 log (1.15)-15 log (1.05) = 0.0001687. and (b) Compute A(0,7) and hence compute the discounted value at t = 0 of a payment of £750 due at t = 7. (c) Compute A(6,7). What is the equivalent constant annual interest rate for the year from t 6 to t = 7? (d) Calculate the constant force of interest that would give rise to the same accumulation from t=0 to t = 10.

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