Friendly’s Quick Loans, Inc., offers you $5.75 today but you must repay $6.75 wh

Question

Friendly’s Quick Loans, Inc., offers you $5.75 today but you must repay $6.75 when you get your paycheck in one week (or else).

What is the effective annual return Friendly’s earns on this lending business? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

If you were brave enough to ask, what APR would Friendly’s say you were paying? (Round answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Friendly’s Quick Loans, Inc., offers you $5.75 today but you must repay $6.75 when you get your paycheck in one week (or else).

Explanation / Answer

We are trying to find the EAR, using the FV equation, as we already know PV and FV.

FV=PV(1+r)

6.75=5.75(1+r)

r= 6.75/5.75-1

r= 0.1739 or 17.39%

To find APR, we multiply the per week rate 17.39% by 52 weeks= 904.35%

EAR= APR[1+ (APR/m)^m]-1

here m=52 weeks

so,

EAR= 904.35 [1+(904.35/52]^52]-1

EAR =417803.79%

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