(a) if $4000 is invested at 5% interest, find the value of the investment at the end of 10 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 is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by a. da dt