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Web Appendix 16B

# Web Appendix 16B - 19819_16Bw_p1-3.qxd 10:41 AM Page 16B-1...

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16B-1 Chapter 16 discussed two common methods of calculating bank interest charges: regular, or simple, interest and add-on interest. However, depending on the nature of the lender and the borrower’s creditworthiness, other loan interest arrangements may be used. This Web Appendix outlines two such loan interest structures: discount interest and compen- sating balances. Discount Interest In a discount interest loan, the bank deducts the interest in advance ( discounts the loan). Thus, the borrower receives less than the face value of the loan. On a one-year, \$10,000 loan with a 12 percent (nominal) rate, discount basis, the interest is \$10,000(0.12) \$1,200. Therefore, the borrower obtains the use of only \$10,000 \$1,200 \$8,800. If the loan were for less than a year, the interest charge (the discount) would be lower; in our example, it would be \$600 if the loan were for six months, hence the amount received would be \$9,400. The effective rate on a discount loan is always higher than the rate on an otherwise similar simple interest loan. To illustrate, consider the situation for a one-year, \$10,000 loan with a 12 percent nominal annual rate, discount basis. Discount interest, paid annually: With a financial calculator, enter N 1, PV 8800, PMT 0, and FV 10000, and then press I/YR to get the effective cost of the loan, 13.64 percent. 1 Now, consider the situation for a three-month \$10,000 loan with a 12 percent nominal annual rate, discount basis. Discount interest, one quarter: Enter N 1, PV 9700, PMT 0, and FV 10000, and then press I/YR to find the periodic rate, 3.092784 percent per quarter, which corresponds to an effective annual rate of 12.96 percent. Thus, shortening the period of a discount loan lowers the effective rate of interest. This occurs because there is a delay in paying interest relative to the longer-term discount loan (\$300 paid each quarter rather than \$1,200 paid up front).

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