財務Assignment

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