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.