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.