(a) If $3000 is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded (i) annually, (ii) semiannually, (iii) monthly, (iv) weekly, (v) daily, and (vi) continuously.
(b) If A(t) is the amount of the investment at time for the case of continuous compounding, write a differential equation and an initial condition satisfied by A(t).