Compounded Interest rates: The magic of compounding - Part II

This is part II of the article Compounded Interest rates: The magic of compounding. Please read the first part of this article before proceeding with this one.

Now suppose you decide to invest 10K each year in stock market and you assume that stock markets are giving 10% returns each year. Quite practical assumption (as proven with the historical returns in the last one decade). So here is how your investment will grow:

Year	Prv Year Carryforward	Annual investment	Total	Interest	Net after Interest
1	-	10,000.00	10,000.00	10%	11,000.00
2	11,000.00	10,000.00	21,000.00	10%	23,100.00
3	23,100.00	10,000.00	33,100.00	10%	36,410.00
4	36,410.00	10,000.00	46,410.00	10%	51,051.00
5	51,051.00	10,000.00	61,051.00	10%	67,156.10
6	67,156.10	10,000.00	77,156.10	10%	84,871.71
7	84,871.71	10,000.00	94,871.71	10%	104,358.88
8	104,358.88	10,000.00	114,358.88	10%	125,794.77
9	125,794.77	10,000.00	135,794.77	10%	149,374.25
10	149,374.25	10,000.00	159,374.25	10%	175,311.67

So your investment in equities or stocks, assumed to be earning 10% each year would grow to 175,311 at the end of year 10. During these 10 years, you would invest a total of 100,000, so your return would be approximately 75% for 10 years.

But, is it really true that investments in equities grow like this? No, not at all. There is no certainty about the returns. So let’s be a bit more practical and have some variability in the earned interest rates for our investments.

Year	Prv Year Carryforward	Annual investment	Total	Interest	Net after Interest
1	-	10,000.00	10,000.00	-10%	9,000.00
2	9,000.00	10,000.00	19,000.00	-5%	18,050.00
3	18,050.00	10,000.00	28,050.00	30%	36,465.00
4	36,465.00	10,000.00	46,465.00	-10%	41,818.50
5	41,818.50	10,000.00	51,818.50	-5%	49,227.58
6	49,227.58	10,000.00	59,227.58	40%	82,918.61
7	82,918.61	10,000.00	92,918.61	5%	97,564.54
8	97,564.54	10,000.00	107,564.54	8%	116,169.70
9	116,169.70	10,000.00	126,169.70	-5%	119,861.21
10	119,861.21	10,000.00	129,861.21	10%	142,847.33

What we see above? When there is uncertainty in the returns or interest rates, our total return value changes. Here we are taking the returns as -10%,-5%,30% and so on. Interestingly, we took high positive returns (40%, 30%, 10%) while we took less negative returns (-5% to a maximum negative of -10%). Still the total maturity amount that we can get is 142,847 only, as compared to 175,311 we discussed in previous case assuming steady returns.

Now the above assumptions are not exactly what may be expected in the markets. But this demonstrates how our faulty assumptions can lead to an uncertain maturity amount. Despite taking high returns for few years (40%, 30%, etc.) our total amount is still less than that in the case of steady 10%. It’s just the timing of the returns that matter.

Keeping the same figures for returns, let’s change the order of returns and bring 40% and 30% in year 1 and 2. We have the following:

Year	Prv Year Carryforward	Annual investment	Total	Interest	Net after Interest
1	-	10,000.00	10,000.00	40%	14,000.00
2	14,000.00	10,000.00	24,000.00	30%	31,200.00
3	31,200.00	10,000.00	41,200.00	-10%	37,080.00
4	37,080.00	10,000.00	47,080.00	-5%	44,726.00
5	44,726.00	10,000.00	54,726.00	-10%	49,253.40
6	49,253.40	10,000.00	59,253.40	-5%	56,290.73
7	56,290.73	10,000.00	66,290.73	5%	69,605.27
8	69,605.27	10,000.00	79,605.27	8%	85,973.69
9	85,973.69	10,000.00	95,973.69	-5%	91,175.00
10	91,175.00	10,000.00	101,175.00	10%	111,292.50

All the figures are same, only the order of interest or returns has changed. Yet we see a drastic fall in total maturity value – it has come down to 111,292.

Take another case, now let’s keep 40% and 30% to year 9 and year 10.

Year	Prv Year Carryforward	Annual investment	Total	Interest	Net after Interest
1	-	10,000.00	10,000.00	-10%	9,000.00
2	9,000.00	10,000.00	19,000.00	-5%	18,050.00
3	18,050.00	10,000.00	28,050.00	-10%	25,245.00
4	25,245.00	10,000.00	35,245.00	-5%	33,482.75
5	33,482.75	10,000.00	43,482.75	5%	45,656.89
6	45,656.89	10,000.00	55,656.89	8%	60,109.44
7	60,109.44	10,000.00	70,109.44	-5%	66,603.97
8	66,603.97	10,000.00	76,603.97	10%	84,264.36
9	84,264.36	10,000.00	94,264.36	40%	131,970.11
10	131,970.11	10,000.00	141,970.11	30%	184,561.14

Now the maturity amount has increased to 184,561.

So what we see here is a huge level of uncertainty in terms of returns. Same return values occurring at different times result in a completely different maturity amounts. It is a well known fact that returns from stock markets are not certain, they are variable. Then, what is the point in claiming that we would get 10% year on year return from the market and so my investment will grow to so and so value. It is difficult for anyone to judge how things will work for returns in stock market. Which year will produce what kind of returns – no one knows.

Take the risk, be aware of the variability and uncertainty. Invest only the real “extra money” in the stock market and exit when your target is achieved.

Tomorrow, I’ll publish another article on the difference between monthly and annually compounded interest rates.

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You may be interested in reading my previous articles. Here is the link to Table of Contents in a chronological order.