Challenge problem · non-routine

Answer: 11 years

1. We need $(1.07)^t \ge 2$.
2. $(1.07)^{10} \approx 1.967$ (not yet double); $(1.07)^{11} \approx 2.105$.
3. So the deposit first doubles in year 11. The 'Rule of 72' estimate $72 \div 7 \approx 10.3$ agrees.