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 $S 5,000$ is invested each year in an annuity earning $9 \%$ annual interest, when will the account be worth $\$ 40,000$ ?

A) $\quad 2.9$ years
B) $\quad 6.3$ years
C) $\quad 14.5$ years
D) $\quad -3.8$ years
E) $\quad 8.0$ years