The “Rule of 70” gives the approximate time T that it takes for an amount of money invested at an annual interest rate of r% to double in value: T=70/r .

1. Write the compound interest formula for a principal P, an annual interest rate r, and a time T, with 2P as the final value of the investment.

2. Solve the equation you wrote in #1 for T by taking “ln” of both sides.
Use the approximation: ln⁡(1+r)≈r, valid for small values of r.

3. Explain why the “Rule of 70” works.