Lizzy,
at any time the money in your account will be A(t)=Pe.07*t where t is the time in years since the deposit took place.
If you want to know how long it took to double your money we have to set A(T)=2P and solve for T, make sense?
So 2P=Pe.07*T is the equation we have for T, notice the P's cancel and taking natural logs of both sides gives
ln(2)=.07*T solving this for T (the time to double) gives T=ln(2)/.07=9.9 years. Th ln(2)=.69 approx.
There is a simple rule if k is the compound growth rate and T is the doubling time then k*T=.69 so if you know either the growth rate or the doubling time you can use this simple equation to estimate the other.
Hope this helps
Jim
