Question

Tom invests $10,000 in a savings account that offers 3.5 percent interest, compounded continuously.
In 10 years Tom will have earned $ in interest, and in years the investment will double. (Use the rule of 70 where required.)

Answer 1

Part 1)
\[A = Pe ^{rt}\]
P = 10,000 r = 0.035 t = 10

Interest = A - P

Answer 2

and in t years the investment will double. (Use the rule of 70 where required.)

A = Pe^rt where A = 2P

2P = Pe^rt divide both sides by P

ln(2) = rt

t = ln(2) / r Solve for t when r = 0.035