The 'quick and dirty' method to ESTIMATE an answer is the 'Rule of 72'. Divide 72 by the interest rate to determine the number of year needed to double the money. That puts the answer at about 10.2 years to double and 20.4 to quadruple. That is close enough to believe the numbers you have are correct.
Substituting 'known' amounts into the formula:
FV = 2 for doubling or 4 for quadrupling.
PV =1
r = 0.07
2 = 1 (1 + 0.07)^t
Edit: MadMan's answr looks right to me.
2 = 1.07^t