Question

If 3000 dollars is invested in a bank account at an interest rate of 6 per cent per year, find the amount in the bank after 12 years if interest is compounded annually
Find the amount in the bank after 12 years if interest is compounded quaterly
Find the amount in the bank after 12 years if interest is compounded monthly
Finally, find the amount in the bank after 12 years if interest is compounded continuously

Answer 1

12 years 3000 *1.06^12

12*4 = 48 quarters
.06/4 = .015
so
3000 * 1.015^48

12*12 = 144 months
.06/12 = .005
3000 * 1.005^144

dx/dt = .06 x
dx/x = .06 dt
ln x = .06 t
x = Xo e^.06 t
x = 3000 e^(.06*12)