Payday loans issued by banks are often referred to as "direct deposit advances." In early 2013, the average direct deposit advance charged $ 10 for a $ 100 advance and was due in 10 days. What is the effective annual rate on this type of loan?

Explanation:

Deposit advance charged $ 10 for a $ 100 advance and was due in 10 days.

The first step in calculation:

10 day rate = FV/PV - 1  = (100+10)/100 - 1 = 0.1 or 10%

FV - future value

PV - present value

The second step in calculation:

annual rate = 10 days rate * 365/10 = 0.1 * 365/10 = 0.1*36.5

=3.65 or 365%

The third step:

EAR = [1+ Quoted annual rate/Compounding period per year(n)]^n - 1 =

= (1+365%/36.5)^36.5 - 1 = 31.42 = 3142%

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