This problem illustrates a deceptive way of quoting interest rates called add$-$on interest. Imagine that you see an advertisement for Crazy Judy$$s Stereo City that reads something like this: $$$$1,180$ Instant Credit! $17\%$ Simple Interest! Three Years to Pay! Low, Low Monthly Payments!$$ You$$re not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Judy explains that if you borrow $$1,180$ for three years at $18\%$ interest, in three years you will owe:

$$1,180\backslash$times $183=$ $$1,180\backslash$times $1\mathrm{.}64303=$ $$1,938\mathrm{.}78$

Now, Judy recognizes that coming up with $$1,938\mathrm{.}78$ all at once might be a strain, so she lets you make $$low$,$ low monthly payments$$ of $$1,938\mathrm{.}78/36=$ $$53\mathrm{.}85$ per month, even though this is extra bookkeeping work for her.

What is the APR $($monthly$)$ on this loan?