If P Dollars Are Invested at the End of Each $$n = \frac { \log \left[ \frac { A r } { P } + 1 \right] } { \log ( 1 + r ) } .$$

If P dollars are invested at the end of each year in an annuity that earns interest at an annual rate r, the amount in the account will be A dollars after n years, where $$n = \frac { \log \left[ \frac { A r } { P } + 1 \right] } { \log ( 1 + r ) } .$$ If $\$ 7,000$ is invested each year in an annuity earning $6 \%$ annual interest, when will the account be worth $\$ 55,000 ?$

A) $\quad 15.3$ years
B) $\quad 6.6$ years
C) $\quad 3.2$ years
D) $\quad - 12.9$ years
E) $\quad 7.9$ years