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CHAPTER 6 B-81 42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the \$1,150 monthly payments is: PVA = \$1,150[(1 – {1 / [1 + (.0635/12)]} 360 ) / (.0635/12)] = \$184,817.42 The monthly payments of \$1,150 will amount to a principal payment of \$184,817.42. The amount of principal you will still owe is: \$240,000 – 184,817.42 = \$55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = \$55,182.58[1 + (.0635/12)] 360 = \$368,936.54 43. We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are: PV of Year 1 CF: \$1,700 / 1.10 = \$1,545.45 PV of Year 3 CF: \$2,100 / 1.10 3 = \$1,577.76 PV of Year 4 CF: \$2,800 / 1.10 4 = \$1,912.44 So, the PV of the missing CF is: \$6,550 – 1,545.45 – 1,577.76 – 1,912.44 = \$1,514.35 The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is: \$1,514.35(1.10) 2 = \$1,832.36 44. To solve this problem, we simply need to find the PV of each lump sum and add them together. It is important to note that the first cash flow of \$1 million occurs today, so we do not need to discount that cash flow. The PV of the lottery winnings is: PV = \$1,000,000 + \$1,500,000/1.09 + \$2,000,000/1.09 2 + \$2,500,000/1.09 3 + \$3,000,000/1.09 4 + \$3,500,000/1.09 5 + \$4,000,000/1.09 6 + \$4,500,000/1.09 7 + \$5,000,000/1.09 8 + \$5,500,000/1.09 9 + \$6,000,000/1.09 10 PV = \$22,812,873.40 45. Here we are finding interest rate for an annuity cash flow. We are given the PVA, number of periods, and the amount of the annuity. We should also note that the PV of the annuity is not the amount borrowed since

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