Question

Friendly's quick loans, inc., offers you $5.25 today but you must repay $6.45 when you get your paycheck in one week (or else). what is the effective annual return friendly's earns on this lending business? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.) effective annual return % if you were brave enough to ask, what apr would friendly's say you were paying? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.) annual percentage rate %

Answer 1

For simplicity, we will assume 52 weeks in a year (instead of 365 days).
The rate of interest per week actually charged is
$6.45/5.25-1$
$=1.2285714-1$
$=0.22857142857$
$=22.85714%$

Effective Annual Rate (EAR) is obtained by compounding the weekly rate for one year (52 weeks)
$EAR=(1+i)^n-1$
$=(1+.228571428571428)^52-1$
$=44546.2997$
=4454629.97%
note: most calculators may not display this value with sufficient accuracy.

The corresponding APR is obtained by multiplying the weekly rate by 52
$APR=52*(6.45/5.25-1)$
$=52(6.45/5.25-1)$
$=11.885714$
=1188.57%