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Compound interest allows you to get an explosive growth of capital. But it can also take a very large part of the future earnings of the investor. When a small change-addition dramatically changes the results of investing.

I call this phenomenon reverse compound interest (or reverse compound interest). Compound interest, on the contrary, has assistants – thieves of our capital (moreover, legal ones).

My task as a long-term investor is to find and neutralize them all (or almost all of them).

## About compound interest

We all more or less know how compound interest works in investments.

- In the first year, interest is charged on the original body of capital.
- In the second year, interest drops on the body of capital and on the interest accrued for the first year (% – No. 1).
- In the third year, interest on the body + on interest (% – No. 1) + on interest for the second year (% – No. 2).
- And so on. Interest on interest on interest on interest ….. and on interest.

In a bank, this is called interest capitalization. In investments – reinvestment of income.

**the main idea**! The investor’s capital will grow a little faster than with the usual calculation of interest income. How much faster?

At the initial stages, the difference will be almost imperceptible. But with an increase in the investment period, this difference will increase every year more and more.

A capital of 100 rubles, invested at a 10% yield, in two years will bring us 120 rubles – if we count as a simple percentage (10 rubles for each year).

Compound interest will allow us to increase our investment by as much as a whole ruble – the end result will be 121.

Growth in the first years will look something like this:

There is a difference in capital between simple and compound interest and even increases slightly every year. But you must admit, the numbers are somehow not impressive.

The rules of 72 and 114 help to understand how compound interest works.

## Rules 72 and 114

**Rule 72** shows how many years it takes for capital to double. You need to divide the number 72 by the annual yield.

For example, with a tenth return, the investor’s capital will double in 7.2 years. With compound interest, we just saved 3 years of investment.

**Method 114** – the meaning is similar to rule 72, only the formula shows how many years the capital will triple.

In our case, a 10% return allows you to triple the initial capital in about 11 years and 5 months. With simple interest, you would have to wait 20 years for a tripling.

The real miracle happens when the investor has a lot of time ahead. Compound interest allows capital to grow exponentially over the long term. Warren Buffett will not let you lie: Buffett was a rogue for the first 50 years of his life.compared to what he currently has. Buffett earned his first billion dollars only after 55.

Buffett on minimum wage – I want to become the second Warren Buffett

The process of capital accumulation itself, taking into account compound interest, will look something like this.

I took the maximum investment horizon of 30 years. I think few people will be able to invest more time.

Well, what can I say: IMPRESSIVE. Due to compound interest, we received capital 3.5 times more!

No wonder Einstein (and according to other sources, Rothschild) called compound interest the “Eighth Wonder of the World.”

## Compound interest in reverse

Now let’s think **what will happen to our capital if we constantly lose part of the profit?** For example, instead of 10% per annum, our yield will be 9%.

Less profitability means less accumulated capital. Is it logical? Yes.

How much less? Logically speaking, the yield has fallen by a tenth: from 10% to 9%, or just 10%. Therefore, at the end of the investment period, our capital will be 10% less.

Is it logical? It seems like yes.

But let’s see what mathematics tells us about this.

We invested money at 10% per annum for 30 years. What we got at the end of the term – we will take as 100% of the capital.

Then:

- The decrease in annual yield from 10 to 9% per annum costs us 25% of capital shortfall.
- If the annual yield drops to 8% per annum, then the investor will “get poorer” by 45% in 30 years.
- With a 7% return, the investor at the end of the term will miss more than half of the capital (56%).

Here are the charts to illustrate.

## The main thieves of capital

Someone will definitely think the following:

*It all looks interesting, of course. But what is the practical meaning of all this? As if someone would specifically want to get not a conditional 10% per annum, but a couple of percent less. This doesn’t happen. This is contrary to common sense. And most investors, I think, are smart and quick-witted.*

OK. Let’s discuss how, from the expected long-term profitability of their investments, the investor, without suspecting it, begins to receive a little less. And end up earning a lot less.

Let’s estimate on the fingers where, how and how much an investor can lose “a lot of money.”

**Broker commissions. **

This is a transaction fee – a percentage, or rather a fraction of a percent, of the transaction amount. The rate can vary from 0% (for example, if you buy the broker’s native funds) to 1% (this is of course an extreme option). And so, the average hospital commission for transactions: 0.05% -0.3%.

Until now, some brokers charge clients additional fees: a minimum fee for each transaction (which can be 30-50 rubles) and a minimum monthly fee (here costs can vary within a few hundred per month).

Can “steal”: up to 1% of the capital.

**Taxes.** The income tax rate is 13%. With an average annual growth of the Russian stock market of shares of 15% per year, it turns out that an investor in taxes can lose up to 2% per year.

Therefore, it is very important to work on tax optimization. Use all available tax deductions (IIS, LDV), do not make thoughtless purchase and sale transactions. In short, by any means try to get away (legally) from income taxes.

Possible losses: 1-2% per year.

**Exchange-traded funds (ETF / BPIF / PIF).**

Do you know what the management fee was for mutual funds before the advent of exchange-traded funds? Interest 5-6% per year. Tin!

Imagine that the average real profitability of the market is 5% per year, and you are forced to pay 6% in the form of commissions. How much do you really earn? Minus one percent a year! A profitable investment, however.

Now, of course, it is a little simpler, BPIF, due to lower commissions, have won their place under the sun. And although there is no talk of any 5-6%, there is still a multiple gap in commissions.

Some funds want half a percent for their services, others a whole percent, others 1.5, or even 2%. At the same time, the size of commissions is in no way connected with the future profitability of the fund. On the contrary, an investor choosing a fund with a high commission is more likely to lag behind funds with a lower management fee in terms of results.

Possible losses: 0.5 – 1% per year.

**Too conservative tools.** Usually in a portfolio, stocks are the engine of growth. Other assets such as bonds, cash, gold act as defensive assets. Too much of them can significantly reduce the overall return of the portfolio. Two or three and even 4% per year can be quite easily missed.

Possible losses: 0.5-4% per year.

**Delay. **It seems to me that one of the main thieves of our capital (albeit implicitly).

What is the point?

Can each year of “non-investment” cost you dearly in the future?

Possible losses: millions / tens of millions.

Here’s a simple example of how much money you can “lose” for delay.

## Riddle about three brothers

Once upon a time there were three twin brothers: Sasha, Pasha and Evdokim.

On the day of his 20th birthday, Evdokim decided to start investing 100 thousand a year in order to form capital from which to live by the age of 50 (people call this movement FIRE).

According to calculations, with a 10% return, Evdokim’s capital should grow to 18 million in 30 years.

A year after the start of investment, Evdokim shared his idea with his brothers – to retire at 50 years old. The brothers liked her. Pasha also started investing 100K in the same year.

At that time, Sasha had outstanding loans, there was no extra money. And he was able to join the brothers only a year later.

**Question:** what capital will Pasha have at the age of 50, who started investing a year later than Evdokim and Sasha, who missed the first two years? The profitability of all brothers is the same and always constant – 10% per year.

If I came across this riddle 15 years ago, I would argue like this:

- Pasha started investing a year later, so he invested 100 thousand less + did not receive a 10% return for this missed year – 10 thousand. This means that his capital will be 110 thousand less than that of Evdokim.
- Sasha has similar calculations, only for two years: 200 thousand is not invested. And not received by interest – 31 thousand. Total capital will be less by 231 thousand.

Right?

No.

**Correct answer:** Pasha’s capital will be 1.65 million less than that of Evdokim, and Sasha – by 3.25 million.

**For those who do not understand.** The catch is that we (I) considered the lost profit for the first (and second) year, but it is necessary for the last (30th) and penultimate (29th).

I think you will agree that over 28 years of investment, the results of the brothers will be the same. The capital will grow to 14.75 million.

At this stage, one of the brothers finished his journey. There are two left. Over the next (29th year), the brothers contributed another 100 thousand. But that’s not the point. Annual 10% yield in just one year increased previously accumulated capital by 1.47 million.

In the last year (30 years) there was one brother who received more than 1.5 million only from interest on capital. In just one year.

A simple year cost more than 1.5 million. And two years – more than 3 million.

## Summarizing

In all sorts of smart books, blogs and investment services, you can find the historical real return on various stock market assets. If we take the stock market, then it varies within 4-6% per annum (above inflation). This is the rate at which long-term investors usually look.

Profitability though real, but it is dirty. In reality, the average investor will almost never get it. In fact, it will always be less, due to the “thieves of capital”. Investors will always suffer from them, bearing annual losses. And according to the rule of compound interest, on the contrary, these losses will grow exponentially. The investor every year will lose (not receive) more and more money.

But it is in the power of the investor to consciously fight the “Thieves” and try to reduce possible losses to a minimum.

Are you fighting the thieves of your capital? Or you think it doesn’t matter!