Example: Nominal and Effective Interest Rate.

A loan shark lends money on the following terms: "If I give you $50 on Monday, you owe me $60 on the following Monday."

(a) What nominal interest rate per year (r) is the loan sharkcharging?
(b) What effective interest rate per year (ia)is he charging?
(c) If the loan shark started with $50 and was able to keep it, as well as all the money he received,out in loans at all times, how much money would he have at the end of one year?

SOLUTION TO PART a

Therefore, i =20% per week.

Nominal interest rate per year =52 weeks x 0.20 = 10.40 = 1040%

SOLUTION TO PART b

SOLUTION TO PART c

With a nominal interest rate of 1040%per year and effectiveinterest rate of 1,310,400%per year, if he started with $50, the loan shark would have $655,200 at the end of one year.