Suppose you borrow $300 from a payday lender for one week at a weekly rate of 10

Question

Suppose you borrow $300 from a payday lender for one week at a weekly rate of 10%. You'll obviously owe $330 at the end of a week. If you are unable to repay the loan, however, the lender will say that you now owe not only $330 but also 10% of that $330 at the end of the second week. Under this scenario, it turns out that after n weeks of not repaying anything you would owe 300 × 1.1n dollars.

Use this formula to determine how much you would owe after 12 weeks. (Round to the nearest cent.)
$   

What total percent interest are you being charged on your 12-week loan? (Round to the nearest percent.)
  %

Explanation / Answer

It is that after n weeks of not repaying anything the borrower would owe 300 × 1.1n dollars.
So after twelve weeks the owed money is 300 × 1.1^12 = 300 x 3.138 = 941.40 dollars.


The borrower is being charged $941.40-$300= $641.40 in interest for twelve weeks.
Suppose 641.40 is x % of 300. Then 641.40 = 300*x% = 300*x/100.
That is 641.40 = 3*x. So x = 641.40/3 = 213.8.

So in total the borrower is being charged 213.8% of the borrowed money by the end of 12 weeks.

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