(a) If 1000 is borrowed at $ 8\% $ interest, find the amounts due at the end of 3 years if the interest is compounded

(i) annually, (ii) quarterly, (iii) monthly, (iv) weekly,

(v) daily, (vi) hourly, and (vii) continuously.

(b) Suppose 1000 is borrowed and the interest is compounded continuously. If $ A(t) $ is the amount due after $ t $ years, where $ 0 \le t \le 3, $ graph $ A(t) $ for each of the interest rates $ 6\%, 8\%, $ and $ 10\% $ on a common screen.