(a) If $1000 is invested at 4% interest, find the value of the investment at the end of 9 years if the interest is compounded as follows. (Round your answers to the nearest cent.) (i) annually $ (ii) semiannually $ (iii) monthly $ (iv) weekly $ (v) daily $ (vi) continuously $ (b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by A(t). dA/dt = Find the initial condition satisfied by A(t). A(0) =