A check-cashing store is in the business of making personal loans to walk-up cus

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 6.5 percent interest per week.

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

Now suppose the store makes one-week loans at 6.5 percent discount interest per week. What’s the APR now? The EAR? (Round your answers to 2 decimal places. (e.g., 32.16))

The check-cashing store also makes one-month add-on interest loans at 6.5 percent discount interest per week. Thus if you borrow $160 for one month (four weeks),the interest will be ($160 × 1.0654 ) – 160 = $45.83. Because this is discount interest, your net loan proceeds today will be $114.17. You must then repay the store $160 at the end of the month. To help you out, though, the store lets you pay off this $160 in installments of $40 per week. What is the APR of this loan? What is the EAR? (Round your answers to 2 decimal places. (e.g., 32.16))

A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 6.5 percent interest per week.

Explanation / Answer

Answer:(A) Here, i = Given interest rate, m = no of payments or compounding in year

1) EAR = (1+i)^m-1 EAR

= (1+.065)^52 - 1

EAR = 25.44%

APR =m*((1+EAR)^(1/m)-1)

= 52*((1+.2544)^(1/52)-1) = 22.72%

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