Question

8. A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 8 percent interest per week.

a.
What APR must the store report to its customers? What EAR are customers actually paying? (Round your EAR answer to 2 decimal places. (e.g., 32.16))

b.
Now suppose the store makes one-week loans at 8 percent discount interest per week. What’s the APR now? The EAR? (Round your answers to 2 decimal places. (e.g., 32.16))

c.

How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a). Assuming 52 weeks a year, then APR = 8%*52 = 416%.

The effective actual rate the consumer pays over a year is

EAR = (1 + r)ⁿ - 1 = (1.08)⁵² - 1 = 54.7060 - 1 = 53.7060, or 5,370.60%

b). In a discount loan, the amount you receive is lowered by the discount, and you repay the full principal. With a 8% discount, you would receive $9.20 for every $10 in principal, so the weekly interest rate would be:

r = [fv / pv]ⁿ - 1[$10 / $9.20]¹ - 1 = 1.0870 - 1 = 0.0870, or 8.70%

APR = 52(8.70%) = 452.17%

EAR = (1 + 0.0870)⁵² - 1 = 76.3894 - 1 = 75.3894, or 7,638.94%

c).