*awarding brainliest* (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) =