Question

9. Compute the weekly interest rate, the APR, and the effective annual interest rate (EAR) earned by CashNow Company if, each week, they make a paycheck loan as follows. On Friday, they give a person $500 in cash and on the next Friday (exactly one week later) they make the person pay them back $550 by signing over their paycheck for that amount. They then relend the money to another person for the week etc, doing this for the full year.

Answer 1

note: some authors consider, 50 weeks constitute an year, some consider 52 weeks constitute an year, the solution has been given for both the assumptions.

interst amount = $550 repaid - 500 lent

=>$50.

weekly interest rate = $50 interest / $500 amount lent *100

=>10%.

APR = 10% per week * 52 weeks per year=>520%.

or alternatively, a few authors only consider 50 weeks in a year, then

APR = 10% *50 weeks =>500%.

EAR.

if 52 weeks per year are considered.

[1+apr/n]^n -1

here,

APR = 520%=>5.2

n = 52 weeks

=> EAR = [1 + 5.2/52]^52 - 1

=>[1.10]^52 - 1

=>141.042932

=>14,104.2932 %.

if 50 weeks a year is considered.

APR =500%=>5

n=50

EAR= [1+5/50]^50-1

=>{1.10]^50-1

=>117.39-1

=>116.39

=>11,639.08%.