Jesse deposits her $500 into bank. interest is 9.5%. she withdraws 737.50. how long did she keep her money in the account?

We'll need to assume that this is a case of compound interest which is paid once per year.

Then    A = P (1 + r)^t becomes

$737.50 = $500 (1+0.095)^t

Then ($737.50/$500) = 1.095^t

Take the log of both sides.  0.1688 = log 1.095^t, or 
                                             0.1688 = t log 1.095 = t(0.0394)

Solving for t,    t = 0.1688/0.0394 = 4.28 years 

This comes out to 4 years and 28/100 of one year, 
or                           4 years and 3.36 months, or
                               4 years, 3 months and 11 days.