(a) If $1000 is invested at 2% interest, find the value of the investment at the end of 8 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.
Find the initial condition satisfied by A.