Question

1. You deposit $3000 in a savings account that pays 4% interest compounding continuously. How much do you have after 20 years?

Answer 1

da/dt = .04 a

da/a = .04 dt
ln a = .04 t + c
a = C e^.04 t
when t = 0, a = 3000
a = 3000 e^.04 t
when t = 20
a = 3000 e^0.8 =3000 * 2.22554 = $ 6676.62