Question

You would like to borrow $1,000 for 4 weeks and have the following options:

1. A payday lender will charge you $10 per $100 borrowed for every week.  
2. A pawnbroker will accept your signed guitar with a value of $2,000 and will charge you a fee of $30 plus 25% EAR interest on the loan compounded weekly plus an additional fee of 20% of the value of the asset for discharge of the loan.
3. Your sister is willing to loan you the money and will only charge you 36% of the principal to be paid with the original loan of $1,000 at the end of the 4 weeks, there is no additional interest or fees. If you don’t pay it back on time though she will tell mom and dad a big secret and you will be kicked out of the house with no place to go besides your aunt’s house that always smells like cabbage. You really don’t want that, she is very strict.

1. Calculate the cost for each option .
2. Calculate the EAR for each option .

Answer 1

a)

Cost of option I

Interest charges = $10/$100*$1000* 4 = $400

Cost of option II

Interest charges = $30 + $1000* ((1+0.25/52)^4-1) + $2000*20% (52 weeks in a year)

= $449.37

Cost of option III

Interest charges = 36%*$1000

= $360

b)

EAR of option I

(1+400/1000)^(52/4) -1 = 78.37147 or 7837.15%

EAR of option II

(1+449.37/1000)^(52/4) -1 = 123.546199 or 12354.62%

EAR of option III

(1+360/1000)^(52/4) -1 = 53.45099 or 5345.10%