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FM27 31 - must make 12 monthly payments of \$9,000 PV = ∑...

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4. In an installment (add-on) loan, the interest is calculated and added on to the required cash amount, and then this sum is the face amount of loan, and it is amortized by equal payments over the stated life. Thus, the interest would be \$100,000 × 0.08 = \$8,000, the face amount would be \$108,000, and each monthly payment would be \$9,000: \$108,000/12 = \$9,000. However, the firm would receive only \$100,000, and it must begin to repay the principal after only one month. Thus, it would get the use of \$100,000 in the first month, the use of \$100,000 - \$9,000 = \$91,000 in the second month, and so on, for an average of \$100,000/2 = \$50,000 over the year. Since the interest expense is \$8,000, the approximate cost is 16 percent, or twice the stated rate: Approximate cost = RECEIVED/2 AMOUNT INTEREST = 000 , 50 \$ 000 , 8 \$ = 0.16 = 16%. To find the exact effective annual rate, recognize that Jaws has received \$100,000 and
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Unformatted text preview: must make 12 monthly payments of \$9,000: PV = ∑ = + 12 1 t t i) (1 PMT 100,000 = ∑ = + 12 1 t t ) i 1 ( 000 , 9 \$ Enter in n = 12, PV = 100000, and pmt = -9000 in a financial calculator, we find the monthly rate to be 1.2043%, which converts to an effective annual rate of 15.45 percent: (1.012043) 12- 1.0 = 0.1545 = 15.45%, which is close to the 16 percent approximate annual interest rate. If the loan were for 90 days: 1. Simple interest . The brothers would have had to pay (0.08/4)(\$100,000) = 0.02(\$100,000) = \$2,000 in interest after 3 months, plus repay the principal. In this case the nominal 2 percent rate must be converted to an annual rate, and the effective annual rate is 8.24 percent: EAR simple = (1.02) 4- 1 = 1.0824 - 1 = 0.0824 = 8.24%. In general, the shorter the maturity (within a year), the higher the effective cost of a simple loan. Mini Case: 27 - 31...
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