The investment P = $1000 and annual rate r = 3.5%.

The annual rate : .

Formula for continuous compounding : .

                       (Substitute P = $1000 and r = 0.035)

The time required for the balance to double, 

                  (Substitute A(P + P =$1000+$1000 = $2000)

             (Divide each side by 1000)

                           (Take natural log of each side)

                             (Apply inverse property: )

                                (Divide each side by 0.035)

The time required for the balance to double is 19.8 yrs. \ \

The formula for n compounding per year: .

n = one year = 12 months.

Substitute P = $1000, t = 10 yrs, n = 12 and r = 0.035.

                           (Evaluate power: ) 

After 10 years, the amount is $1418.91.

The time required for the balance to double is 19.8 yrs, and

After 10 years, the amount is $1418.91.