Question

Friendly's Quick Loans, Inc., offers you $3.20 for $4.20 or I knock on your door." This means you get $3.20 today and repay $4.20 when you get your paycheck in one week (or else) a. If you were brave enough to ask, what APR would Friendly's say you were payina? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What's 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.) Answer is complete but not entirely correct. APR EAR 10.00 3.52 % %

Answer 1

Solution:

a. APR

First of all we have to find the interest rate, as we know the present value and future value.

Using the future value equation: FV = PV(1+r)

$4.20 = $3.20(1+r)

1+r = 4.2/3.2

r = 1.3125 - 1

r = 0.3125

r = 31.25% per week

The interest rate per week is 31.25%. To find the APR we have to multiply this rate with number of weeks in a year

APR = (52) 31.25% = 1,625%

APR = 1,625%

we know that for calculating EAR:

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

Here m = number of weeks

EAR = [ 1 + (1,625/52)]^52 - 1

EAR = [ 1 + 0.3125]^52 - 1

EAR = 138,408,967.22 - 1

EAR = 138,408,966.22% (approximately)