Question

Friendly’s Quick Loans, Inc., offers you "three for four or I knock on your door." This means you get $3 today and repay $4 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 paying? (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 1

Answer:

APR 13%

effective rate 13.64%

Explanation:

we know that the rate compounding weekly generates:

$3(1+r) = 4$

we solve for rate:

r = 4/3 - 1 = 0.25

this will e the rate compounding weekly.

There is 52 weeks per year so APR = 52 x 0.25 = 13%

while the effective rate will be:

$(1 + \frac{0.13}{52})^{52} = 1 + r_e$

effective rate 0.13864