Question

A check cashing store is in the business of making personal loans to walk up customers the store makes only one week loans at 7% interest per week what a PR must the store report to its customers? What EAR are the customers actually paying?

Now suppose the store makes one week loans at 7% discount interest per week. What's the APR now? The EAR?

The check cashing store also makes one month out on interest loans at 7% discount interest per week though Us if you borrow $260 for one month (4 weeks), The interest will be ($260 x 1.07 to the fourth power)-$260=80.81. because this is discount interest your net loan proceeds today will be $179.19. You must then repay the store $260 at the end of each month. To help you out though the store let you pay off this $260 in installments of $65 per week what is the APR of this loan? What is the EAR?

Answer 1

Part 1:

Data Available = one-week loans at 7% interest per week

Percentage Return also is known as Annual Percentage Return is calculated as

APR = r * m

r = interest rate

m = frequency of compunding

Hence APR = 7% * 52

= 364%

EAR = (1 + (stated annual interest rate)/ m ) ^m-1

= (1 + 364/(52*100))^52 - 1

= 33.7253 - 1   

= 32.7253

Part 2: To calculate APR and EAR for discounted interst rate

Effective rate = (discounted interest rate) / (100 - 100* discounted intereest rate)

= 0.07/(1 - 0.07) = 0.0752 = 7.52%

Hence APR = 7.52 * 52 = 391.39

EAR = (1 + (stated annual interest rate)/ m ) ^m-1

= (1 + 391.39/(52*100))^52 - 1

= 43.39 - 1   

= 42.39

Part 3

Total amount to be repaid = 260 USD

Weekly instalment = 65 USD

Effective value of the loan taken = 179.19 USD

Interest paid = 80.81 USD. Yearly interest paid = 969.72

Average Loan Balance = 179.19/2 = 89.895

EAR = 969.72 / 89.89 = 1078.78 %

EAR = (1 + (stated annual interest rate)/ m ) ^m-1

1078.78 = (1 + APR/(52*100))^52 - 1

APR = (1078.78 + 1) ^ (1/52) - 1

= (1.1437 - 1) * 52

= 14.37% * 52

= 747.5331%