A bank pays interest at an annual rate of 4% compounded continuously. How long will it take for your money to double?

Question

Give 3 decimal places in your answer and include units. 

Answer 1

1. The formula for Continuous Compound Interest is A = Pe^rt, where A = amount after time t, P = principal at the time of deposit, r = the decimal form of the annual interest, and t = years.

2. A = 2P

3. 2P = Pe^rt

4. 2 = e^rt

5. ln 2 = rt

6. ln 2 = (.04) t

7. ln 2/.04 = t

8. t ≈ 17.329 years

Answer 2

17.329 years