Question

You take a $1,000 post-dated check to a “PayDay” lender. The lender charges you a $10 application fee and loans you $975. The check matures five (5) days after you allow the lender to possess it. What is the APR for this loan if you only use this service one time? What is the APR (and APY) if you use this service over and over such that you repeated 73 times in the year?

Answer 1

Fees F=10

Loan L=975

Paymen P=1000

Let r be the 5 days rate

P/(1+r)=L-F

1000/(1+r)=975-10

r=3.63%

If loan is paid once then APR = 365*r/5 =73*3.63% =264.77%

if loan is paid 73 times in a year then APR = (1+r)^73-1 =(1+3.63%)^73-1=1247.43%