BA 350 - 1 The Lexington Property Development Company has a...

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1. The Lexington Property Development Company has a $10,000 note receivable from a customer due in three years . How much is the note worth today if the interest rate is a. 9%? b. 12% compounded monthly? c. 8% compounded quarterly? d. 18% compounded monthly? e. 7% compounded continuously? SOLUTION: PV = FV [PVF k,n ] a. PV = $10,000 [PVF 9,3 ] = $10,000 (.7722) = $7,722 b. PV = $10,000 [PVF 1,36 ] = $10,000 (.6989) = $6,989 c. PV = $10,000 [PVF 2,12 ] = $10,000 (.7885) = $7,885 d. PV = $10,000 [PVF 1.5,36 ] = $10,000 (.5851) = $5,851 e. FV = PV (e kn ) $10,000 = PV [e .07(3) ] $10,000 = PV [1.2337] PV = $8,105.70 Future Value of an Amount – Example 6.1 (page 246) 2. What will a deposit of $4,500 left in the bank be worth under the following conditions: a. Left for nine years at 7% interest? b. Left for six years at 10% compounded semiannually? c. Left for five years at 8% compounded quarterly? d. Left for 10 years at 12% compounded monthly? SOLUTION: FV = PV [FVF k,n ) a. FV = $4,500 [FVF 7,9 ] = $4,500 (1.8385) = $8,273.25 b. FV = $4,500 [FVF 5,12 ] = $4,500 (1.7959) = $8,081.55 c. FV = $4,500 [FVF 2,20 ] = $4,500 (1.4859) = $6,686.55 d. FV = $4,500 [FVF 1,120 ] = $4,500 (3.3004) = $14,851.80 Finding the Interest Rate – Example 6.3, (page 250) 3. What interest rates are implied by the following lending arrangements? a. You borrow $500 and repay $555 in one year. b. You lend $1,850 and are repaid $2,078.66 in two years.
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c. You lend $750 and are repaid $1,114.46 in five years with quarterly compounding. d. You borrow $12,500 and repay $21,364.24 in three years under monthly compounding. (Note: In c and d, be sure to give your answer as the annual nominal rate.) SOLUTION: FV = PV [FVF k,n ] a. $555 = $500 [FVF k,1 ] FVF k,1 = 1.1100 k = 11% b. $2,078.66 = $1,850.00 [FVF k,2 ] FVF k,2 = 1.1236 k = 6% c. $1,114.46 = $750.00 [FVF k,20 ] FVF k,20 = 1.4859 k = 2% k nom = 8% d. $21,364.24 = $12,500.00 [FVF k,36 ] FVF k,36 = 1.7091 k = 1.5% k nom = 18% Solving for the Number of Periods – Example 6.4 (page 251) 4. How long does it take for the following to happen? a. $856 grows into $1,122 at 7%. b. $450 grows into $725.50 at 12% compounded monthly. c. $5,000 grows into $6724.44 at 10% compounded quarterly. SOLUTION: PV = FV [PVF k,n ] a. $856 = $1,122 [PVF 7,n ] PVF 7,n = .7629 n = 4 years b. $450.00 = $725.50 [PVF 1,n ] PVF 1,n = .6203 n = 48 months = 4 years c. $5,000 = $6,724.44 [PVF 2.5,n ] PVF 2.5,n = 0.7436 n = 12 quarters = 3 years 5. Sally Guthrie is looking for an investment vehicle that will double her money in five years. a. What interest rate, to the nearest whole percentage, does she have to receive? b. At that rate, how long will it take the money to triple? c. If she can't find anything that pays more than 11%, approximately how long will it take to double her investment?
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d. What kind of financial instruments do you think Sally is looking at? Are they risky?
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