The Boston Globe on New Year's Day 2009 reported that a New Hampshire law will cap the interest rate on payday loans at 36 percent per year.

"Payday lenders typically chard $20 per $100 for two-week loans backed by the borrower's car title or next paycheck. That amounts to 1.43 percent interest per day, an annual rate of 521 percent." [R267]

The cap will limit the daily rate to about 0.1 percent, so just $1.38 -- a dime a day -- on that two week $100 loan.

(a) What is a "payday loan"? (b) Verify the computation that 1.43% interest per day is 521% interest annually.

(c) If the 1.43% interest is compounded daily then the true annual rate of interest is in fact much more than 521%. How much is it?

(HINT: Start with the calculation (1+0.0143)365\left(1+0.0143 ight)^{365}(1+0.0143)365. The answer is hard to believe.)

(d) Verify that paying interest of $1.38 on a two-week loan of $100 is just about a "dime a day" and corresponds to a daily interest rate of about a tenth of a percent. What annual rate does that represent?

(e) Visit a payday loan website and report on what you discover there about interest rates.