Question

I was able to do part a but i need help with part b:

a) If $4000 is invested at 5% interest, find the value of the investment at the end of 8 years if the interest is compounded as follows.
(i) annually $5909.82
(ii) semiannually $5938.02
(iii) monthly $5962.34
(iv) weekly $5966.15
(v) daily $5967.14
(vi) continuously $5967.30

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.

I though it was 0.04(4000)(t) but that's wrong

Answer 1

(vi) A = 4000e^.05t
dA/dt = 200 e^.05t
so
dA/dt = 0.05 A
or
dA = 0.05A dt