A “cash-advance” store provides customers with a service making one-week loans at 8% interest per week.
(a) What APR are the loans issued at? How much is the EAR that customers actually are paying?
(b) If instead the store makes one-week discount loans at 8 percent (discount) interest per week, what are the APR and the EAR?
(c) As a way to diversify the products offered, the store just started offering a modified one-month add-on interest loans at 8% discount interest per week. These new loans work in such a way that if you borrow $100 for one month (four weeks), the interest is ($100 × 1.084 ) − 100 = $36.05. Since this is discount interest, the net loan proceeds today are $63.95. Nevertheless, you must repay $100 at the end of the month. In order to help the customers, the store lets them pay off the $100 owed in installments of $25 per week. What is the APR of such loans? What is the EAR?