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.

iii) Determine the constant eective rate of interest per annum, to the nearest 1%, which would lead to the same result as in part ii) being obtained.

iv) Calculate the present value of an annuity of 1000 paid at the end of each of years two and nine.