Friendly’s Quick Loans, Inc., offers you “$3.60 for $4.60 or I knock on your doo

Question

Friendly’s Quick Loans, Inc., offers you “$3.60 for $4.60 or I knock on your door.” This means you get $3.60 today and repay $4.60 when you get your paycheck in one week (or else). If you were brave enough to ask, what APR would Friendly’s say you were paying? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

APR % _________

What’s the effective annual return Friendly’s earns on this lending business? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

EAR % ______

Explanation / Answer

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

4.6=3.6(1+r/100)

Hence r=(4.6/3.6)-1

=0.2778(Approx)

Hence APR=(0.2778*52)=1444.44%(Approx)

EAR=(1+APR/m)^m-1
where m=compounding periods

=(1+0.2778)^52-1=34,330,169.09(Approx).

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