An interesting article a while back at:
http://www.news.com.au/money/money-matters/meet–the-lenders-charging-780-per-cent/story-e6frfmd9-
1225875224705
It says that one payday lender charges 30% for a two week loan (14 Days).
This raises a couple of interesting questions:
1. What is the nominal annual interest rate for such a loan?
2. What is the effective annual interest rate for such a loan?
It is very important to make the distinction between nominal and effective rates in finance so I would be interested
to see others views on this.
Regards
Dr. Fitzsimmons
The nominal interest rate is the periodic interest rate times the number of periods per year. Therefore, a
nominal interest rate of 30% based on weekly compounding means a 15% (30%/2) interest rate per
week and 780% (30% x 26) per year.
The effective interest rate attempts to describe the full cost of borrowing. It takes into account the
effect of compounding interest, which is left out of the nominal or “stated” interest rate.
The formula to calculate the effective rate of interest is given by r = (1 + i/n)^n – 1. In this formula, r
represents the effective interest rate, i represent the stated interest rate, and n represents the number
of compounding periods per year. Therefore considering that the compounding is done once every two
weeks, r = (1+0.3/26)^26-1 = 34.75%.
The effective rate of interest is always higher than the nominal interest rate since it also considers the
compounding factor. In the present case, while the nominal rate for a 2 week period loan is 30%, the