Save-Your-Day loans advertises no-interest loans of $100 on which only a $1 fee

Question

Save-Your-Day loans advertises no-interest loans of $100 on which only a $1 fee per week is charged. Collateral is usually a car title. The borrower will not pay anything until the loan is paid off. Then the amount to be paid back is $1.00 for each week per $100 of loan value.   For a loan of $200 (two loans of $100) for 3 weeks, the pay back amount would be $200 + $1.00 * 2 loans * 3 weeks = $200 + $6= only $206. Louie borrows $500 and pays it back in 4 weeks. What effective annual rate will Save-Your-Day earn on the loan to Louie? Save-Your-Day loans advertises no-interest loans of $100 on which only a $1 fee per week is charged. Collateral is usually a car title. The borrower will not pay anything until the loan is paid off. Then the amount to be paid back is $1.00 for each week per $100 of loan value.   For a loan of $200 (two loans of $100) for 3 weeks, the pay back amount would be $200 + $1.00 * 2 loans * 3 weeks = $200 + $6= only $206. Louie borrows $500 and pays it back in 4 weeks. What effective annual rate will Save-Your-Day earn on the loan to Louie?

Explanation / Answer

Payback amount= 500+1*5*4=$520

Lets assume frequency of compounding to be week

Let effective annual rate for compunding weekly be r

500*(1+r)^4/52=520

(1+r)^1/13=1.04

1+r=1.04^13=1.665

r=.665

r=66.5%

Effective Annual Rate=66.5%

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