3. * 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 and £230 at t = 10. = 0 accumulates to £210 at t = 5 (a) Show that 1 4 a = 15 1 b = 250 log (1.05) log (1.15) - 3 log(1.15) 0.008352, 1 125 = 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.