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Suppose that the parents of a young child just born decide to make annual deposit into a saving account, with the first deposit being made on the child's 5th birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the child is able to make five equal... 顯示更多 Suppose that the parents of a young child just born decide to make annual deposit into a saving account, with the first deposit being made on the child's 5th birthday and the last deposit being made on the 15th birthday. Then, starting on the child's 18th birthday, the child is able to make five equal withdrawals $20,000 until his 22nd birthday. If the interest rate is 8% during this period of time, what should the annual deposits be in years 5 to 15? 更新: 請詳例計算方法
最佳解答:
Let $D be the annual deposit from the fifth birthday to the fifteen birthday Present value of the deposit = $D x {1 – [(1 + 8%) ^ (-11)]} x (1 + 8%) / 8% Present value of the withdrawal from the eighteen birthday to the twenty-second birthday = $20,000 x {1 – [(1 + 8%) ^ (-5)]} x (1 + 8%) / {8% x [(1 + 8%) ^ 13]} = $20,000 x {1 – [(1 + 8%) ^ (-5)]} / {8% x [(1 + 8%) ^ 12]} Hence, $D x {1 – [(1 + 8%) ^ (-11)]} x (1 + 8%) / 8% = $20,000 x {1 – [(1 + 8%) ^ (-5)]} / {8% x [(1 + 8%) ^ 12]} $D = $20,000 x {1 – [(1 + 8%) ^ (-5)]} / {1 – [(1 + 8%) ^ (-11)]} / [(1 + 8%) ^ 13] = $20,000 x 0.3194 / (0.5711 x 2.7196) = $20,000 x 0.2056 = $4,112.95 Birthday Cash Flow Discounted Cash Flow 5 -$4,112.95 -$4,112.95 6 -$4,112.95 -$3,808.29 7 -$4,112.95 -$3,526.19 8 -$4,112.95 -$3,264.99 9 -$4,112.95 -$3,023.14 10 -$4,112.95 -$2,799.21 11 -$4,112.95 -$2,591.86 12 -$4,112.95 -$2,399.87 13 -$4,112.95 -$2,222.10 14 -$4,112.95 -$2,057.50 15 -$4,112.95 -$1,905.09 18 $20,000.00 $7,353.96 19 $20,000.00 $6,809.22 20 $20,000.00 $6,304.83 21 $20,000.00 $5,837.81 22 $20,000.00 $5,405.38 S $0.00
其他解答:D1B39E804036C6BD
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