How many years will it take for a $50 investment to grow to $1000 if it is compounded continuously at a rate of 5%?

A(t) = P • e^(r)(t)

Question

How many years will it take for a $50 investment to grow to $1000 if it is compounded continuously at a rate of 5%?

A(t) = P • e^(r)(t)

agreene · Answer

1000 = 50 e^(0.05t)    Divide both sides by 50
20 = e^0.05t                natural log each side
ln(20) = ln(e^0.05t)    
ln(20) = 0.05t               divide by 0.05
ln(20)/0.05=t               simplify
20ln(20) = t                  evaluate if you want a real number
59.9146 years = t                    :)