Cash never rests: compound interest

19.12.2020 | Financial Education

This session was compiled on the basis of a text by Dr. Andrzej Fesnak, EFC (European Financial Consultant), Master Trainer (an expert in teaching an effective combination of sound practice and creative theory) specializing in the fields of financial education and project financing, also a noted assistant professor and journalist in Business and Economics, a qualified financial advisor and real estate broker, and the director of one of the oldest and most famous training companies in Poland.

In this session, we will look at financial engineering, which shows how even a small amount of money, well utilized, can become a powerful means of achieving wealth and financial freedom. This is only a small slice of the advanced creative thinking in financial mathematics that is presented in detail by Dr. Andrzej Fesnak, EFC (European Financial Consultant) in his educational publications. I hope that this session will inspire you to take up an active study of finance, to the point where, as Robert Kiyosaki might put it, you are employing your money to work harder for your benefit. Because, when you think of it, we generally work for money without even realizing it: we might as well make that work more effectively for us!

Albert Einstein is often quoted as having remarked that compound interest is the greatest invention in history. And whether the great physicist actually ever said it or not, compound interest really is the key mechanism in the multiplication of money.

If we loaned someone $1,000 for 10 years at 7.5% simple interest, we would emerge with $1,075 – but applying compound interest, we would arrive at $2,061.03.

This explains why mathematical tables were produced and prized for many years, to calculate the multiplication of capital by means of compound interest. In advanced societies, these began to be replaced as early as 1990 by financial calculators (e.g. HP 10 BII, HP 17 BII+) – business-specific utilities that could make
complex, advanced calculations in a matter of tens of seconds. But in the peaceful Republic of Bliss, far removed from the leading lights of financial education and other forms of civilization and progress – thinking about finances along the lines of the old mathematical tables or time-consuming mathematical calculations (such as paper-based multiplication and long division) seems still to have relevance today.

Let us now go back to a basic table of calculations that shows the mechanism of compound interest on a scale from 1% to 20%:

Rate (%) Capital-doubling period (rounded) Rate (%) Capital-doubling period (rounded)
1% 70 years 11%    6.5 years
2% 35 years 12%    6 years
3% 23.5 years 13%    5.75 years
4% 18.5 years 14%    5.5 years
5% 14.5 years 15%    5 years
6% 12 years 16%    4.5 years
7% 10.5 years 17%    4.5 years
8% 9 years 18%    4.25 years
9% 8 years 19%    4 years
10% 7.5 years 20%    3.75 years


The main conclusions to be drawn from this table are fairly straightforward:

  • When you start an investment, the capital-doubling period depends greatly on the rate of interest.
  • Banks generally work in the range 3%-6%, which means that the doubling of the capital takes from 12 to 24 years. When capital gains tax is also taken into consideration, this period will extend further.

In guides to personal financial planning, the recommendation is generally to look for investments with a minimum 12% interest per year, as optimal for your personal finances. Why? If we refer to the table above, the answer is easy to work out. If we assume that in Western countries a person’s economically active life lasts for something like 42 years, this means that we have an overall total of seven six-year periods (7 x 6 = 42).

What arises from this? Well, if we invest at 12% per year, during our professional career we can double our capital seven times over. So how much will this make?

This question can be answered in the next table. Let us take a specific example. What would happen if, on this model, a 24-year-old man invested $1,000 at 12% a year and kept the money invested until he was 66 years of age?

Phase (in six-year periods) Age Amount produced
First 6 years 24 – 30    2,000
Second 6 years 31 -36    4,000
Third 6 years 37 – 42    8,000
Fourth 6 years 43 – 48    16,000
Fifth 6 years 49 – 54    32,000
Sixth 6 years 55 – 60    64,000
Seventh 6 years 61 – 66    128,000
Grand total:    128,000


Whereas, if you invest at only 3-4% per year, then over the same 42 years you will double the capital twice over: i.e. £1,000 will turn into $2,000 in approximately 20 years, and after the second 20 years you will end up with £4,000.

If you have some knowledge of the mathematics, you will know that the difference in effect is that between 22 and 27:

22 (2 squared) gives 4, whereas 27 (2 to the power of 7) produces 128: so we are talking of a difference between 4 times as much, and 128 times as much. This difference between “4 x more” and “128 x more” is certainly no mere arithmetical abstraction. It is plain enough for anyone to understand – and probably enough to stimulate anyone’s imagination.

Nevertheless, compound interest can contain some traps as well, which should be noted.


When more is less.

How can more mean less, in the present context? There are several reasons why this may be so – we will now discuss two of the major ones.

First, it depends on the taxation scales that apply.

For example:

If someone earned up to £12,000, they might have paid 19% tax.

Between £12,001 and £30,000, this may have risen to 30% tax.

From £30,001 upwards, they might find their income reduced by 40% tax.

The riddle of tax thresholds may create many paradoxes in our financial lives. Here’s one: you earn £1,000 per month. After tax, you have £810 net. A benevolent boss awards you a pay raise of £100 per month. You now earn £1,100, but after 30% tax deduction (£1 100 – £330) you take home only £770. An ‘increase’ of £100 actually results in £40 less in your pay packet!

If you earn £2,500 per month, after tax you are left with £1,750. You receive a pay rise of £100 per month which results in £2,600 per month. The tax on this amount is £1,040, so you are left with only £1,560. In this case £100 ‘more’ results in £190 less in your account!

Here’s a second example, more strictly related to compound interest:

Urban Bank suggests an investment with an annual capitalization of 5.88%, while Metro Bank proposes one with a monthly capitalization of 5.83%. Which gives you more? The monthly capitalization will mean that, effectively, you gain +6.02% per year. It seems than that there is virtually no difference, because 6.02% – 5.88% = 0.14%. And $10,000 x 0.14% = £14. Or in plain English, on your investment of £10,000, the final difference is a paltry £14.

But here, everything depends on scale. Imagine instead that you invested not £10,000, but £100 million. The final difference now is “only” £140,000. This is worth thinking about.

When longer is not worse.

Let’s do an analysis of compound interest in the next example. You know the saying: the best loan is the shortest one.

A very cautious married couple earns a total of £6,000 per month, and spends £3,000 a month on living costs. They need a loan of $300,000: the interest rate is 7%. They want the shortest possible loan, and take it out for 13 years. Their monthly installment is £2,934.22. After 13 years they will be free of any further loan repayments. The interest by then will have amounted to £157,738.79, or about 53% of the loan.

And what would happen if they took the same loan, but over 30 years? Probably unwise, because the monthly installment goes down to £1,995.91, but the interest over 30 years goes up to about £418,525.69. And in addition, this means 30 years of debt.

In this case, we have a repayment difference of about $1,000 per month.

To produce £418,525.69 over 30 years by investing at 7% per annum, you need to invest £343.06 per month. On this model, you “recover” the interest and have approximately £650 per month at your disposal. True, it is over a longer loan period: but look at the effect of applying a model that balances out the loan installment with regular investment. (To remind yourself of the principles of safe borrowing, please review Session 8 of our course).

Sometimes a larger debt cuts down the cost

Let’s say you need £100,000, and you borrow it as a loan for 10 years, at 10% interest. Monthly installments amount to £1,321.51. If instead you took out a loan for £150,000, then the installments would be £1,982.26. If you can afford such a solution, and you invest the extra £50,000 from the £150,000 you borrowed for 10 years at 8% per year, after 10 years your investment will have grown to £107,946.25.

Even a quick calculation reveals that after 10 years you would have paid off £237,871.20 (£1,982.26 x 120), and you would have accumulated £107,946.25 in your account – a net difference of £129,924.95.

This means that the entire loan would have cost you only £29,924!

And if you obtained an interest rate of 16.88% on your £50,000 investment, you would have had the loan for free.

Let’s consider an example from geometry to illustrate a key point. A rectangle measuring 10m by 2m amounts to an area of 20m2. An alternatively-proportioned rectangle of 4m x 5m, or one measuring 8m x 2.5m, or even a circle with a radius of 2.52m all make up the same area: 20m2.

This example gives us the important clue that you can vary the time, alter the interest rate and juggle the amounts of a loan in various ways, to get a desired result.

Remember: Keep improving your financial management skills as much as you can!


Now complete task:

Using insights from this session, calculate how, using the ‘magic’ of compound interest, you can buy an apartment in the metropolis affordably (in other words, at a price you can manage)!


To learn more about this personal finance management course please visit this website

The Financial Manifesto

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