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The Power of Compounding - Compound Interest

"Compounding interest is the greatest mathematical discovery of all time". Albert Einstein

There is a story about an Emperor of China who was so excited about the game of chess that he offered the inventor of the game one wish. The inventor replied that he wanted one grain of rice on the first square of the chess board, two grains on the second square, four on the third and so on through the 64th square. The unwitting emperor agreed to the modest request. But two to the 64th power is 18 million trillion grains of rice - more than enough to cover the entire surface of the earth. The Emperor, realizing that he had been duped, had the inventor of the game beheaded.

Eighteen million trillion is a huge number. I personally can't even picture the number of zero's after the 18 in my head. I'm sure that many people are overwhelmed by the thought of retirement and think that they need eighteen million trillion dollars in their RRSP to retire comfortably.

This is not the case. A comfortable retirement is within the grasp of most of us provided that we start early and use compounding to our favour. A real life example illustrates this.

I recently answered an email from a visitor to my site
http://www.rrsp.org who was very concerned that she would not have enough to retire with. It was her goal to have enough money at age 60 to pay herself $50,000 per year. She was 33 years old, had $50,000 in an RRSP and planned to contribute $5,000 per year until age 60. Fortunately I built a simple spreadsheet for these kind of questions. Let's look at the numbers assuming a 10% growth rate:

Growth Rate:

 

 

10%

 

 

 

Opening Balance:

 

 

$50,000

 

 

 

Yearly Increment:

 

 

$5,000

 

 

 

Age

 

 

33

 

 

 

 

 

 

 

 

 

 

 

Yr

Age

Open Bal

Increment

Sub-Total

Closing Balance

 

1

33

$50,000

$5,000

$55,000

60,500

 

2

34

60,500

$5,000

$65,500

72,050

 

3

35

72,050

$5,000

$77,050

84,755

 

4

36

84,755

$5,000

$89,755

98,731

 

5

37

98,731

$5,000

$103,731

114,104

 

6

38

114,104

$5,000

$119,104

131,014

 

7

39

131,014

$5,000

$136,014

149,615

 

8

40

149,615

$5,000

$154,615

170,077

 

9

41

170,077

$5,000

$175,077

192,585

 

10

42

192,585

$5,000

$197,585

217,343

 

11

43

217,343

$5,000

$222,343

244,577

 

12

44

244,577

$5,000

$249,577

274,535

 

13

45

274,535

$5,000

$279,535

307,488

 

14

46

307,488

$5,000

$312,488

343,737

 

15

47

343,737

$5,000

$348,737

383,611

 

16

48

383,611

$5,000

$388,611

427,472

 

17

49

427,472

$5,000

$432,472

475,719

 

18

50

475,719

$5,000

$480,719

528,791

 

19

51

528,791

$5,000

$533,791

587,170

 

20

52

587,170

$5,000

$592,170

651,387

 

21

53

651,387

$5,000

$656,387

722,026

 

22

54

722,026

$5,000

$727,026

799,729

 

23

55

799,729

$5,000

$804,729

885,202

 

24

56

885,202

$5,000

$890,202

979,222

 

25

57

979,222

$5,000

$984,222

1,082,644

 

26

58

1,082,644

$5,000

$1,087,644

1,196,409

 

27

59

1,196,409

$5,000

$1,201,409

1,321,549

 

28

60

1,321,549

$5,000

$1,326,549

1,459,204


It's hard to imagine a scenario where this person would not be able to withdraw $50,000 per year with this kind of money accumulated. In fact, this is what would happen to age 69 taking out $50,000 per year:

Growth Rate:

 

 

10%

 

 

 

Opening Balance:

 

 

$1,420,954

 

 

 

Yearly Increment:

 

 

-$50,000

 

 

 

Age

 

 

61

 

 

 

 

 

 

 

 

 

 

 

Yr

Age

Open Bal

Increment

Sub-Total

Closing Balance

 

1

61

$1,420,954

-$50,000

$1,370,954

1,508,049

 

2

62

1,508,049

-$50,000

$1,458,049

1,603,854

 

3

63

1,603,854

-$50,000

$1,553,854

1,709,240

 

4

64

1,709,240

-$50,000

$1,659,240

1,825,164

 

5

65

1,825,164

-$50,000

$1,775,164

1,952,680

 

6

66

1,952,680

-$50,000

$1,902,680

2,092,948

 

7

67

2,092,948

-$50,000

$2,042,948

2,247,243

 

8

68

2,247,243

-$50,000

$2,197,243

2,416,967

 

9

69

2,416,967

-$50,000

$2,366,967

2,603,664

The minimum RRIF withdrawal is about $128,000, or about two and a half times the $50,000 that she was hoping to withdraw. This is an enviable position to be in.

If you have microsoft Excel, you can access the spreadsheet that performed these calculations here:
http://www.rrsp.org/spreadsheets.htm - click on the "Investment Growth" link. Have fun - Doug Hudson.