Question

Friendly’s Quick Loans, Inc., offers you “twelve for seventeen or I knock on your door.” This means you get $12 today and repay $17 when you get your paycheck in one week (or else).

If you were brave enough to ask, what APR would Friendly’s say you were paying? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What’s the effective annual return Friendly’s earns on this lending business? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Effective rate of interest = ($17 - $12)/$12 * 100 = 41.67%

This is weekly interest rate. Now, considering 52 weeks in a year,

Annualized Percentage Rate (APR) = 41.67*52 = 2166.84%

Effective Annual Return = (1 + 41.67%/52)^52 - 1

= (1.008013)^52 - 1

= 1.514394 - 1

= 0.514394

= 51.44%