Calculations to show how much Olga needs to accumulate for retirement.

Retirement/Income Investment Analysis
Prepared for Olga

Initial Investment:

60,000.00

Annual Investments:

8,484.79

Inflation:

3.00 %

Deposit Indexation:

3.00 %

Interest Growth:

9.00 %

 

Year

Age

Present Value Deposits

Actual Deposits

Total Value of Investment

Present Value of Investment

1

42

68,484.79

68.484.79

74,648.43

72,474.20

The calculation is quite understandable: In year 1, the annual investment of $8,484.79 is added to the initial $60,000 she has saved by age 42. The resulting $68,484.79 earns $6,163.63, what makes the year-end total of $74,648.43. In terms of today's money (that is, considering t he 3% inflation) this is worth $72,474.20.

2

43

8,484.79

8,739.34

90.892.66

85.675.05

So that to keep the purchasing power of the money constant, the actual deposit in year 2 is increased by 3% (hopefully, Olga's nominal income also keeps pace with inflation). $74,648.43 + $8,739.79, at 9% growth rate, earns $7,504.94, making the total $90,892.66 by the end of year 2. (In today's terms it is worth only $85,675.05 though.)

3

44

8,484.79

9,001.52

108,884.65

99,644.88

The calculation can be done in the same fashion in the consecutive years until...

4

45

8,484.79

9,271.56

128,790.28

114,428.49

5

46

8,484.79

9,549.71

150,790.59

130,073.28

6

47

8,484.79

9,836.20

175,083.20

146,629.42

7

48

8,484.79

10,131.29

201,883.79

164,150.00

8

49

8,484.79

10,435.23

231,427.73

182,691.18

9

50

8,484.79

10,748.29

263,971.85

202,312.44

10

51

8,484.79

11,070.73

299,796.41

223,076.69

11

52

8,484.79

11,402.85

339,207.20

245,050.50

12

53

8,484.79

11,744.94

382,537.83

268,304.34

13

54

8,484.79

12,097.29

430,152.28

292,912.77

14

55

8,484.79

12,460.21

482,447.61

318,954.70

15

56

8,484.79

12,834.01

539,856.97

346,513.64

16

57

8,484.79

13,219.03

602,852.84

375,677.96

17

58

8,484.79

13,615.60

671,950.60

406,541.16

18

59

8,484.79

14,024.07

747,712.39

439,202.23

19

60

8,484.79

14,444.79

830,751.33

473,765.88

20

61

8,484.79

14,878.14

921,736.12

510,342.94

21

62

8,484.79

15,324.48

1,021,396.06

549,050.71

22

63

8,484.79

15,784.22

1,130,526.50

590,013.30

23

64

8,484.79

16,257.74

1,249,994.82

633,362.06

... Olga reaches the retirement age. From then, she will continuously deplete her capital. The numbers in brackets below indicate this.

You Retire

Present Value Income

Actual Income

Investment Balance

Interest Now
6%

24

65

(35,000.00)

(69,075.53)

1,251,774.45

615,790.08

Because of inflation, when she starts using her accumulated capital, she has to withdraw $69,075.53 to be able to buy the same amount of goods and services she pays only $35,000 for today. Her remaining capital will still earn interest, but the amount of that will be lessening, therefore the investment balance will show an accelerating decline.

25

66

(35,000.00)

(71,147.79)

1,251,464.26

597,706.30

26

67

(35,000.00)

(73,282.23)

1,248,872.95

579,095.80

27

68

(35,000.00)

(75,480.69)

1,243,795.79

559,943.25

28

69

(35,000.00)

(77,745.12)

1,236,013.72

540,232.86

29

70

(35,000.00)

(80,077.47)

1,225,292.42

519,948.38

30

71

(35,000.00)

(82,479.79)

1,211,381.39

499,073.09

30

71

(35,000.00)

(84,954.19)

1,194,012.83

477,589.78

32

73

(35,000.00)

(87,502.81)

1,172,900.62

455,480.75

33

74

(35,000.00)

(90,127.90)

1,147,739.09

432,727.76

34

75

(35,000.00)

(92,831.73)

1,118,201.80

409,312.06

35

76

(35,000.00)

(95,616.69)

1,083,940.22

385,214.36

36

77

(35,000.00)

(98,485.19)

1,044,582.33

360,414.78

37

78

(35,000.00)

(101,439.74)

999,731.15

334,892.88

38

79

(35,000.00)

(101,482.93)

948,963.11

308,627.62

39

80

(35,000.00)

(107,617.42)

891,826.43

281,597.36

40

81

(35,000.00)

(110,845.94)

827,839.31

253,779.80

40

81

(35,000.00)

(114,171.32)

756,488.07

225,152.03

42

83

(35,000.00)

(117,596.46)

677,225.10

195,690.44

43

84

(35,000.00)

(121,124.36)

589,466.79

165,370.74

44

85

(35,000.00)

(124,758.09)

492,591.22

134,167.95

45

86

(35,000.00)

(128,500.83)

385,935.82

102,056.34

46

87

(35,000.00)

(132,355.85)

268,794.76

69,009.43

47

88

(35,000.00)

(136,326.53)

140,416.33

35,000.00

48

89

(35,000.00)

(140,416.33)

0.00

0.00

By the time Olga turns 90, her capital is all used up. This is quite an uncomfortable, nevertheless, not very unlikely, scenario. If we also add the fact that this calculation was made with quite - actually, overly - optimistic growth assumptions (since those 9% and 6% rates should be after-tax values), then the proposition of the need to save at the level of $8,484 annually seems strongly warranted.
If we change our growth assumptions to a more realistic 6% for the whole 48 year period, it makes the annual saving amount needed as $15,649.13 to reach the same goal, ... an amount that can easily make Olga feel uncomfortable.

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