43. We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, andsubtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cashflows we know are:PV of Year 1 CF: $1,700 / 1.10 = $1,545.45PV of Year 3 CF: $2,100 / 1.103 = $1,577.76PV of Year 4 CF: $2,800 / 1.104 = $1,912.44So, the PV of the missing CF is:$6,550 – 1,545.45 – 1,577.76 – 1,912.44 = $1,514.35The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The valueof the missing CF is:$1,514.35(1.10)2 = $1,832.3644. To solve this problem, we simply need to find the PV of each lump sum and add them together. It is important tonote that the first cash flow of $1 million occurs today, so we do not need to discount that cash flow. The PV of thelottery winnings is:PV = $1,000,000 + $1,500,000/1.09 + $2,000,000/1.092 + $2,500,000/1.093 + $3,000,000/1.094+ $3,500,000/1.095 + $4,000,000/1.096 + $4,500,000/1.097 + $5,000,000/1.098+ $5,500,000/1.099 + $6,000,000/1.0910PV = $22,812,873.4045. Here we are finding interest rate for an annuity cash flow. We are given the PVA, number of
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