Jennifer just turned 23 and can save $500 per quarter, starting in three months. if jennifer can earn 7% compounded quarterly, what age will she be when she accumulates $1,000,000?

This is a straight savings problem. The formula required is the one you use to find the sum of a geometric sequence. I find it useful to consider the last deposit first.

The last deposit earns no interest. It is $500.
The next-to-last deposit earns 1 quarter's interest, so it contributes
.. $500*(1 +.07/4) = 500*1.0175
to the sum.
The deposit before that contributes
.. $500*1.0175²
to the sum.
Clearly, the sum is that of "n" terms of a geometric sequence with first term 500 and common ratio 1.0175. Your job is to find "n" that makes the total be $1 million and then convert that number of quarters to Jennifer's age.

The sum of "n" terms of a geometric sequence with first term "a" and common ratio "r" is given by
.. S = a*(r^n -1)/(r -1)
We can solve this for n.
.. S*(r -1)/a +1 = r^n
.. n = log(S*(r -1)/a)/log(r)
.. n = log(10⁶*(0.0175)/500 +1) / log(1.0175)
.. n ≈ 206.559

The balance in Jennifer's account will reach $1,000,000 when Jennifer makes her 207th payment. She will be 74 3/4.