A while ago, a rather sneaky car salesman tried to sell me a car financing deal, advertising an 'incredibly low' annual interest rate of 1.5%. What he later revealed that this was the 'flat rate' (meaning the interest is charged on the original balance, and doesn't decrease with the balance over time).
The standard for advertising interest is APR (annual percentage rate), where the interest charged decreases in proportion to the balance. Hence the sneaky!
I was able to calculate what the interest for the flat rate would be (merely 1.5% of the loan, fixed over the number of months), but I was unable to take that total figure of interest charged and then convert it to the appropriate APR for comparison.
I'm good with numbers but not a mathematician. To the best of my knowledge I would need to use some kind of trial and error of various percentages (a function that oscillates perhaps?) to find an APR which most closely matched the final interest figure.
What would be the most appropriate mathematical method for achieving this?
Please feel free to edit this question to add appropriate tags - I don't know enough terminology to appropriately tag the question.