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Attached Problems and Solutions, required in Excel with formulas.

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Fiancial Management 1 Problem 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. 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 [FVFk,n] a. $555 = $500 [FVFk,1] FVFk,1 = 1.1100 k = 11% b. $2,078.66 = $1,850.00 [FVFk,2] FVFk,2 = 1.1236 k = 6% c. $1,114.46 = $750.00 [FVFk,20] FVFk,20 = 1.4859 k = 2% knom = 8% d. $21,364.24 = $12,500.00 [FVFk,36] FVFk,36 = 1.7091 k = 1.5% knom = 18% Problem 4: How long does it take for the following to happen? Fiancial Management 2 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 [PVFk,n] a. $856 = $1,122 [PVF7,n] PVF7,n = .7629 n = 4 years b. $450.00 = $725.50 [PVF1,n] PVF1,n = .6203 n = 48 months = 4 years c. $5,000 = $6,724.44 [PVF2.5,n] PVF2.5,n = 0.7436 n = 12 quarters = 3 years Problem 6: Branson Inc. has sold product to the Brandywine Company, a major customer, for $20,000. As a courtesy to Brandywine, Branson has agreed to take a note due in two years for half of the amount due, and half in cash. a. What is the effective price of the transaction to Branson if the interest rate is: (1) 6% (2) 8% (3) 10% (4) 12%? b. Under what conditions might the effective price be even less as viewed by Brandywine? Solution: a. 1) PV = FV [PVF6,2] = $10,000 (.8900) = $8,900 $8,900 + $10,000 = $18,900 Effective Discount = 5.5% 2) PV = FV [PVF8,2] = $10,000 (.8573) = $8,573 Fiancial Management 3 $8,573 + $10,000 = $18,573 Effective Discount = 7.1% 3) PV = FV [PVF10,2] = $10,000 (.8264) = $8,264 $8,264 + $10,000 = $18,264 Effective Discount = 8.7% 4) PV = FV [PVF12,2] = $10,000 (.7972) = $7,972 $7,972 + $10,000 = $17,972 Effective Discount = 10.1% b. The discount from Brandywine's viewpoint is calculated as in part a) however, using the interest rate at which that firm borrows. If Brandywine's rate is higher than Branson's, it will observe a greater discount. Problem 10: How much will $650 per year be worth in eight years at interest rates of a. 12% b. 8% c. 6% Solution: FVA = PMT [FVFAk,n] a. FVA = $650 [FVFA12,8] = $650 (12.2997) = $7,994.81 b. FVA = $650 [FVFA8,8] = $650 (10.6366) = $6,913.79 c. FVA = $650 [FVFA6,8] = $650 (9.8975) = $6,433.38 Problem 18: Sam Rothstein wants borrow $15,500 to be repaid in quarterly installments over five years at 16% compounded quarterly. How much will his payment be? Solution: Fiancial Management 4 For quarterly compounding we have k = knom/12 = 16%/4 = 4% n = 5 years x 12 months/year = 60 months. Write equation of 6.19 and substitute. PVA = PMT[PVFAk,n] $15,500 = PMT[PVFA4,60] Using Appendix A-4 $15,500 = PMT[22.6235] PMT = $685 Problem 21: Construct an amortization schedule for a 4 year, $10,000 loan at 6% interest compounded annually. Solution: PVA = PMT [PVFAk,n] $10,000 = PMT [PVFA6,4] PMT = $2,885.92 Year 1 2 3 4 Beg Bal ($) 10,000.00 7,714.08 5,291.00 2,722.54 PMT ($) 2,885.92 2,885.92 2,885.92 2,885.92 Int ($) 600.00 462.84 317.46 163.35 Prin Recd ($) 2,285.92 2,423.08 2,568.46 2,722.54 End Bal ($) 7,714.08 5,291.00 2,722.54 0.00