Eddie wrote a $280 check to a check holding company. which gave him $260 in cash. After two weeks the company will cash his $280 check. What is the annual simple interest rate for this loan?

1 Answer

Roughly 200%

Explanation:

The amount of interest being charged is $20 #(=280-260)#. The $20 is #20/260=1/13~=7.7%# of the amount he is given.

Eddie has the use of the $260 for 2 weeks before the check is cashed, meaning that the interest isn't collected for 2 weeks (with the cheque being cashed).

To find the annual simple interest rate, we can use a ratio (52 weeks being roughly equivalent to 1 year):

#(2 " weeks")/"interest rate for 2 weeks"=(52 " weeks")/"interest rate for 52 weeks"#

#2/.077=52/x#

#2x=4.004=>x=2.002=>200.2%#

To give some sense of this answer, credit card companies in the USA are limited by law to charging (I believe) 39.6% interest per year.