2. The force of interest, (t), is a function of time and at any time t, measured in years, is given by

(t) = 0.05 0 t 3 0.09 0.01t 3 < t 8 0.01t 0.03 8 < t.

i) Determine the accumulation factor A(0, t) for 0 < t 3 and determine A(0, 10). ii) If 500 is invested at t = 2 and a further 800 at t = 9, calculate the accumulated amount at t = 10.