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

Multiple Choice

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 $\$ 6,000$ is invested each year in an annuity earning $10 \%$ annual interest, when will the account be worth $\$ 45,000$ ?

A) $\quad - 3.0$ years
B) $\quad 2.8$ years
C) $\quad 5.9$ years
D) $\quad 13.5$ years
E) $\quad 7.5$ years