Currency functions. Compound interest formulas Contribution to the formation of the compensation fund

Sergey A. Alferov

Unit of value and currency

Once one author, solving the issue of organizing the monetary system, proposed to issue money for the release of products at the cost at the time of production ... That is, to combine the pricing at enterprises and the emission of funds. This combination of micro-economics and macro-economics is of course not true. But our interest is not in a detailed criticism of this, let's move on.

The topic of pricing also leads to the following questions. The unit of currency and the unit of value: how and what is related here? .. Could there be a unit of value? If yes, then what is its measure? And what is value in the economy?

Usually, it is suggested to put some “values” or some “goods” in the basis of the currency (as security, in the “standard of value”). From the point of view of the economy (in economic terms) they are one and the same, just different names for a “resource” that has a high price and liquidity; moreover, it is traded, that is, it has an unstable value. Opponents of such "super-market" say that no commodity of "variable value" can be a measure of value, can not provide a unit of measurement for money. And of course they are right; in addition to this correctness, let us add, as they said, that one commodity (one value) located within the economy cannot be equivalent to (measure) the entire value of the economy.

Let's try to talk about all this from scratch; and not from someone else's position.

So, we understand this natural scientific desire to have "natural scientific measures" in the economy as well ... In general, the most fundamental measures underlying all other units of measurement are the measures of time (t) and measures of length (l). The units of mass (m) are the second on the level of fundamentalness; next are temperatures (T °). (This is approximately how the world appeared: first time and space, then mass and temperature.)

What is measurement? It is a comparison of two characteristic values ​​related to the same phenomenon, one of which is a reference (verification value). Or, in other words, measurement is a comparison of 2 values ​​of a characteristic immanently inherent in the measured object (phenomenon). Moreover, these characteristics are the result of the interaction of the object with the outside world (including the tool of cognition), the result of its manifestation. The question is - what are the qualities (characteristics) we compare? And what kind of relationships, interactions do they reveal? So - in the general case.

The severity expresses the interaction of 2 massive bodies. And how in these coordinates will the phenomenon of value be, what interacts here? What affects the value of the cost? And here is the first difference from physics. We have not one value, but two. First, it is costly, or prime cost. And, secondly, the exchange, or "sale price".

Let's define what influences these values. But only not through the equal sign, but through the proportionality sign. (If we put an equal sign, then it will be unreasonable "objectification", learning.)

"Cost value" ~ TxL, where T - time spent, L - material costs.

"Exchange value" ~ TxLxMxt °, where M - consumer qualities, t ° - the degree of rarity (value).

Moreover, the parameter “ M »Can both increase the cost and decrease it.

Can we and should we eliminate the influence of the last 2 parameters? It is better (for everyone, including the economy) if the parameters are not eliminated, but improved ...

So, we have 2 nd values ​​and 2 nd prices, and the last one - the one that will be credited throughout the economy - is determined in the process of exchange. And here the question of immanence arises ... Now we will come to this, but for now we will continue.

Measurement is comparison; and comparison is competition. How! The economic process is based on a kind of "metrological process" ... And the economy for the birth and awareness of society is also fundamental, as a measurement for understanding the world ... So what is the peculiarity of "economic metrology"?

First, it happens through exchange, not through production. At the same time, production and exchange in holistic economy inseparable. Moreover, the peculiarities of their interaction typify the economy. But when we talk about some economic phenomenon, we must refer it to our half. The sphere of production is also the sphere of the micro-economy. The sphere of exchange is the sphere of macroeconomics. This is how roles and meanings crossed. Casus vivendi. Ce la vie. So, the "general economic value" is formed during the exchange.

And then we formulate, as a principle: "Cost is a comparison of 2 products" ... The measure of a commodity is another commodity. Hence everything. This includes distortion through the temptation of an incomplete person. Hence the modern extremes, the extremes that created the quasi-economy. The real economy is integral by definition. And she is a challenge to integrity. A challenge through a crisis brought about by an incomplete person.

Product comparison is product competition. True competition and the market are fundamental to the economy. Because theirs are real - and d O it is false to the state to protect without regard to "merits". Why d O it is false to define the principles of this market, the principles and mechanisms of this development. In principle, this is what the book is about. And with this began Adam Smith himself.

In theoretical economics (political economy), the initial object is the commodity, and the main phenomenon is value 1. Because it is an immanent property of goods. Then the main unit of the economy should be the unit of value. And what exactly is a unit of value, a standard of value? Let's continue.

The amount of value is determined at the time of exchange. Price Is an immanent characteristic goods... But she is not an immanent characteristic. product! “Cost value” has nothing to do with the metaphysics of macroeconomics ... Here nonlinearity appears, moreover, the uncertainty associated with the inclusion and dependence on upper-level processes in society.

We have already seen above that the peculiarity of the economy, as natural process is such that the standard of value is the product itself ... But this is not yet a complete, not a practical answer to the question about the unit of value (because we do not yet know this product, if it exists, of course). And there is still no answer about the unit of currency. Our last shot concentrates on understanding what "Product" we are talking about? That is, to solve our problem of finding the measure of the entire economy, we must determine the specificity of the measured value of this "Product"; what does this "single Product" itself measure? And the clue will almost be there if you again understand the requirement of the time for the ability of a person to manage in a holistic manner, the requirement for knowledge and consciousness.

The epoch, through the economy, exposes a person, firstly, an account, and, secondly, a demand ... The economy is subject. But not subjective; because it also has its own metaphysics, its own principles. An absolute, rational-administrative "schedule" in the economy is harmful. As well as for a person. In economics, there will always be "subtleties" that can only be solved "here and now." Through understanding such a dual nature of the economy (which has both "ethics" and freedom), through such a mirror, a person passes through another understanding of himself, an understanding of the characteristics and measure of his social nature. This is what meant the presence of the last quadrant of economics before the return to man on a new round in the quadra “Existence of the community” (see Chapter II).

We inevitably reduce ourselves by defining value when pricing at the level of the micro-economy, when it seems like the process of creating a product and forming prices through costs and sets the appearance of a certain amount of money. The definition of economic value and product pricing should not be confused. The cost, including the price, should be determined by the owner of the goods. There can be no direct administrative-centralized pricing. The state must regulate this area (it must, by forming a real market) differently (see below, the “profitability corridor”.)

And now the answers.

The unit of value is given by the entire real economy as a whole, all goods and services in general! It gives, as the ratio of the entire mass of goods in circulation that has received the price to the "volume of accounting certificates" of these values, that is, to the volume of money (to the money supply). This happens at every moment of the metaphysical economic movement; and with a certain degree of adequacy ("uncertainty"), allowed by the prevailing Culture and Technology, there should be monitoring of commodity and money supply.

That is, both tool creation and measurement are both - but not as with micro-level pricing. Here, relying on the already established "status quo" (and without creating positive feedback effects by sharp managerial movements, inconsistent in response time in the system), a rather inertial total economic value is measured and, at the same time, the amount of money (or the "price of division" of money) is specified; for which the mediator-criterion is precisely the natural-scientific meters of energy consumption in the economy as a whole.

The instrument affects the measurement - we are already familiar with this from the physics of the microworld. And here the behavior strategy is very similar.

Thus, with this understanding of the integral economy, as the basis of the actual unit of its measurement, we also understand that the unit of value is the unit of the existing money supply.

Let us denote the duality of the situation of this "quantum economy" in more detail.

At any given moment, we can accurately determine the total value in the economy; but at the same moment the unit in which we determined this value will be different.

At every moment we can accurately determine the value (commodity) content of the monetary unit; but at the same moment the total cost in the economy will be different.

The measurement of value is provided (set) by a certain value of the monetary unit, which in turn depends on the total value. Also in the physics of elementary particles, we are not able to simultaneously know (measure) two mutually influencing parameters (characteristics) of a particle. For example, due to the impact on the system of an elementary particle with a comparable "pico-meter" (in magnitudes of the order of 10 -15, and we do not have smaller instrumentation), we can accurately measure at one moment only one of two: or the location (coordinate) , or speed; and due to constant changes (fluctuations) of energy, while measuring it, we cannot reliably know at the same time the exact time for this energy value, moreover, acting on the system with an increase in the accuracy / speed of measurement, we change the energy of the system and do not achieve an improvement in the overall accuracy ...

The last "moreover" does not apply to the economy as a macro-sphere. And this gives hope for the possibility of effective expenditure of efforts to achieve the required accuracy in the system of parameters "total cost - monetary unit". And all the rest of "relativity" has a complete analogy.

True, one can also say so about the difference between uncertainties in the pico- and macro-world. In the pico-world, uncertainty is nevertheless associated with the absence of the necessary class, the order of meters, operating with an incomprehensible level of characteristics of space, time and energy. And there probably won't be such material measures. In economics, we have (the first, but maybe not the only one in the macro-sphere) uncertainty associated with a high level of synergy in the social sphere, in the spiritual sphere. As always, only the subject contains such uncertainty ... But both there and there we came to the boundaries of the spiritual world, to the boundaries of integrity.

By the way, in the aforementioned pairs of uncertainties with simultaneous measurements in the nano-world in each pair there are, according to the first degree of fundamentality: the parameter of time and the parameter of space. And the second member of each pair is associated with mass - a measure of the 2nd degree of fundamentality. The fact that energy is associated with mass, that they are two related manifestations of materiality, is understandable. And I will explain with the first uncertainty. On the right side of the proportionality sign to the product of the measurement accuracy in the coordinate and velocity, there is "mass" as a coefficient in the denominator. That is, shifting the "mass" to the left, we compare the accuracy of measuring the coordinate and momentum; as the first Heisenberg uncertainty is sometimes interpreted.

But back to the economy. So, for the main topics of economics, we state that we are not able to know simultaneously and absolutely exactly the parameters of the pair “total value - monetary unit”. But with thin approximations and small iterations, we can achieve quite acceptable accuracy, an acceptable match of about 1%. The inflation-free currency will be already at 3-5% (corresponding to normal economic growth). For comparison, now banks are allowed to issue loans with only 30% of their own funds.

Now, when the discrepancy between the commodity and money supply reaches several times, it sounds like fantasy (and I hope it will not be criticized as insufficient). In fact, this is the norm. A forgotten, distorted norm, the return to which through the necessary social institutions and mechanisms is a return to normal life.

Let's return briefly to the second, "cost value". The construction of a developed, complex economy (its mechanisms) from one of 2 types of values ​​generates along a chain of interconnections of economic and power mechanisms, that is, logically - exactly 2 types of economy: centrally planned (bureaucratic) and "popular". Moreover, American capitalism, building itself on hidden mechanisms and interests, goes into the 1st category. For this, he undermined the "exchange value" by the discrepancy between the "unit of value" and the "unit of the dollar"; the value of the dollar began to be assigned, which in fact meant administrative pricing and manipulation; that is, “cost” and “printing press” began to have “meaning” ... And the USSR in the first half of the 50s, in terms of meanings and decisions, had an economy of the second type. He came to this in a difficult way, and great breakthroughs awaited him, but ... But the realization of what was already groped did not take place; there was no understanding, theory (and such tasks were set by Stalin). The oak ideology of Marxism buried everything. At the same time, in the 50s, taking into account precisely the “cost value”, the country became a common corporation; after which a person should have received economic rights within the framework of this single economic space (if then they understood everything ... but we, Russians, will come to this). This was not done, and the bureaucracy and the pure (ideologically pure) 1st type of economy quickly gained the upper hand. And when, in the 60s, within the framework of the formed bureaucracy of the 1st type of economy, they began to introduce an alien concept and mechanisms of profit, then the system collapsed.

USA and USSR: each entered from its side, and had its own way of distortion. They came to an impasse; the more quickly, the more they would be left to themselves. The accounting system from the “cost value” quickly led to bureaucratization (this logic of management constructions is easy to see, we suggest you do it yourself). And then only the will and knowledge of the leader, and the availability of time could lead the people to freedom. The market system from the "exchange value" put profit at the forefront, which, crossing certain limits, gave rise to the whole bouquet of human passions. Received the right, having money; and it logically ends before our eyes. And it ends with even more bureaucracy; and the bureaucracy of the soul ... And now the reckoning is only on the people, on their awareness of all experience; on finding the middle path, on the correct choice of the parameters of this path ...

Let us repeat, when we understand the integral economy as the basis of the actual unit of its measurement, we get that the unit of value is the unit of the existing money supply. And from here follows the next important thing.

We can say that each currency has a certain economic space; and a healthy economy (and a corresponding social organism) should be associated with only one currency. When moving to another economic space, there should be a change of currency (and about the rules for this - see the chapter on fair inter-economic relations).

Power always relies on a certain economic space, its own economic space. And a real economy (which has not rejected its metaphysics) always needs real government regulation. Power and economy - the real ones - are a whole while maintaining their own characteristics. In this whole, the temptation to misuse features is manifested. And this temptation is removed only when this whole is in a certain goal-setting, when there are meanings, values, criteria. When the power-economy is in the context of a single, integral nation, is in its support and its content, in its service. And only a single nation in its values ​​and meanings, in its service to the highest, is a certain guarantee of healthy relations between power and economy.

1 But what is most interesting is that the construction of even systemic mechanisms of the real economy can do without appealing to questions of value. Apparently, beyond the scope of this question, everything real is just beginning. But it does not end and follows, as it happened with the ideologists from the economy, starting with Marx (who, by the way, simply transferred the conclusions of the micro-level to the macro-level, he changed it and "did not notice").

Sergei A. Alferov, Unit of value and monetary unit // "Academy of Trinitarianism", M., El No. 77-6567, publ. 15994, 12.07.2010


So, to determine the value of property that brings income, it is necessary to determine the current value of money that will be received at some time in the future.

It is known, and in conditions of inflation, it is much more obvious that money changes its value over time. The main operations that make it possible to compare money of different times are accumulation (accumulation) and discounting operations.

Accumulation- this is the process of bringing the current value of money to its future value, provided that the invested amount is held in the account for a certain time, bringing periodically accumulated interest.

Discounting Is the process of bringing cash flows from investments to their present value.

In the assessment, these financial calculations are based on a complex process, when each subsequent accrual of the interest rate is carried out both on the principal amount and on the unpaid interest accrued for previous periods.

In total, six functions of the monetary unit are considered, based on compound interest. To simplify the calculations, tables of six functions have been developed for known rates of income and the accumulation period (I and n), in addition, you can use a financial calculator to calculate the desired value.

1 function: The future value of the monetary unit (the accumulated amount of the monetary unit), (fvf, i, n).


If charges are made more often than once a year, then the formula is transformed into the following:

k- frequency of savings per year.

This function is used when the present value of money is known and it is necessary to determine the future value of a monetary unit at a known rate of return at the end of a certain period (n).

Forex classes are wonderful for you to prepare for successful work in the international currency market Forex!

Rule 72x

For an approximate determination of the doubling time of capital (in years), it is necessary to divide 72 by the integer value of the annual rate of return on capital. The rule is valid for rates from 3 to 18%.

A typical example for the future value of a currency is a problem.

Determine how much will be accumulated on the account by the end of the 3rd

years, if today you put in an account that brings 10% per annum, 10,000

FV = 10000 [(1 + 0.1) 3] = 13310.

2 function : Present unit value (present value of the reversion (resale)), (pvf, i, n).

The present unit value is the inverse of the future unit value.

If interest is accrued more often than once a year, then

An example of a problem is the following: How much you need to invest today in order to get 8000 on the account by the end of the 5th year, if the annual rate of return is 10%.


Function 3 : The present value of the annuity (pvaf, i, n).

An annuity is a series of equal payments (receipts) spaced from each other by the same period of time.

There are regular and advance annuities. If payments are made at the end of each period, then the annuity is normal, if at the beginning - advance.

The formula for the present value of a regular annuity is:

PMT - equal periodic payments. If the frequency of charges exceeds 1 time per year, then

Upfront Annuity Present Value Formula:

Typical example:

The lease agreement for the summer cottage is drawn up for 1 year. Payments are made monthly at 1000 rubles. Determine the present value of lease payments at a 12% discount rate if a) payments are made at the end of the month; b) payments are made at the beginning of each month.


4 function : Accumulation of monetary unit for the period (fvfa, i, n).

As a result of using this function, the future value of a series of equal periodic payments (receipts) is determined.

Payments can also be made at the beginning and end of the period.

Regular annuity formula:

Typical example:

Determine the amount that will be accumulated on an account that yields 12% per annum by the end of the 5th year, if 10,000 rubles are deposited annually into the account a) at the end of each year; b) at the beginning of each year.

5 function : Currency depreciation contribution (iaof, i, n) The function is the reciprocal of the present value of a regular annuity. The amortization contribution for a monetary unit is used to determine the amount of the annuity payment to repay a loan issued for a certain period at a given loan rate.

Depreciation is a process defined by this function and includes the interest on the loan and the payment of the principal.


For payments made more often than once a year, the following formula is used:

An example is the following task: Determine what payments should be in order to repay a loan of 100,000 rubles by the end of the 7th year, issued at 15% per annum.

6 function : Reimbursement fund factor (sff, i, n)

This function is the inverse of the function of accumulating a unit over a period. The reimbursement fund factor shows the annuity payment that must be deposited at a given percentage at the end of each period in order to receive the desired amount after a given number of periods.

To determine the amount of the payment, the following formula is used:

For payments (receipts) made more often than once a year:

An example would be a task.

Determine what the payments should be so that by the end of the 5th year you have 100,000 rubles on an account that yields 12% per annum. Payments are made at the end of each year.

The annuity payment specified by this function includes the payment of principal without interest payments.

Present value of the currency - the second function of money. The idea is to give an estimate of the present value of the money that can be received at the end of a certain period at a given discount rate. Determined by the formulas:

a) when calculating interest once a year:

b) when calculating interest more often than once a year:

(7)

PV - real cost, rubles;

FV - future value, rubles;

The factor of the present value of the unit;

k - the number of charges per year (period).

Task 2 ... Determine the current value of 5250 rubles, which will be received at the end of 6 years at a 12% rate. Accrual on a quarterly basis.

Solution:

Answer: PV = 2609.09 rubles.

Accumulation of monetary unit for the period - the third function of money. The economic meaning of this function is how much will be accumulated on the account at a given rate if one currency is regularly deposited into the account for a certain period of time.

PMT - Periodic Equal Amount Payment.

1. Calculating the future value of a regular annuity

a) for accruals at the end of each year:

(8)

b) for accruals carried out more often than once a year:

(9)

2. Calculation of the future value of the advance annuity (at the beginning of the year, month)

(10)

b) for payments made more often than once a year:

(11)

Objective 3. Determine the amount that will be accumulated on an account that brings 12% per annum by the end of the 16th month, if you save 2,000 rubles on a monthly basis.

a) at the end of the month;

b) at the beginning of the month.

Solution:

a) formula (9)

b) formula (11)

Answer: a) FV = 34766.63 rubles.

b) FV = 34,422.41 rubles.

Compensation fund

Compensation fund fourth function of money. This function shows how much needs to be deposited into the account regularly over a certain period of time in order to have one currency on the account by the end of this period at a given rate of return.

a) for payments made once a year:

(12)

(13)

Reimbursement fund factor.

Problem 4 ... Determine the amount of payments so that by the end of 16 years you have 20,000 rubles on an account that yields 11% per annum. Payments are made:

1) annually k = 1,

2) monthly k = 12.

Solution:

2)

Answer: 1) PMT = RUB 510.33

2) PMT = RUB 38.47

Unit depreciation contribution

Depreciation contribution - the fifth function of money. Depreciation in this case is understood as the process of debt repayment over time. This function shows what should be the annuity or equal payments to repay a loan in one currency, issued at a certain percentage for a certain period. The function is used to determine the mandatory periodic payments required to repay (return) a loan within a specified period.

a) for payments made once a year:

(14)

b) for payments made more than once a year:

(15)

Problem 5 ... A loan in the amount of 130,000 rubles was issued for 6 years at 15% per annum. Determine the amount of annuity payments. The loan is repaid monthly.

Solution:

Answer: PMT = RUB 2748.85

The current value of the annuity

The current value of the annuity is the sixth function of money. Meaning - what is, at a given discount rate, the current value of a series of equal payments in one currency over a certain period of time.

Annuity - a series of equal payments made at the same time interval can be regular and advance.

This function is the inverse of the depreciation function for the depreciation of the unit. Used to determine the present value of recurring payments received in the future over a period of time.

Calculating the present value of a regular annuity(payments are made at the end of the period).

a) for payments made once at the end of the year:

(16)

To determine the value of an investment project or property, it is necessary to determine the current value of money that will be received some time in the future. In an inflationary environment, money changes its value over time. The main operations that make it possible to compare money of different times are the operations of accumulation (accumulation) and discounting.

Accumulation - it is the process of bringing the present value of money to its future value, provided that the invested amount will be in the account for a certain time, bringing periodically accumulated interest.

Discounting - the process of bringing cash receipts from investments to their present value.

1 function. Determine the future value of the monetary unit (accumulated amount of monetary units)

FV is the future value of the monetary unit,

PV - the present value of the monetary unit,

i - rate of return,

n is the number of accumulation periods in years.

Task. Determine what amount will be accumulated on the account by the end of 3 years, if today you put 10 thousand rubles into the account at 10% per annum.

2 function. Present value of the currency (present value of the resale reversal)

Task... How much should be invested today in an investment project in order to receive 8 thousand rubles by the end of 5 years. The rate of return is 10%.

3 function. Determination of the present value of the annuity.

Annuity Is a series of equal payments (receipts) spaced from each other for the same period of time.

There are regular and advance annuities. If payments are made at the end of each period, then the annuity is normal; if in the beginning - advance.

The formula for the present value of a regular annuity is:

PMT - equal periodic payments.

Task. The lease agreement for the summer cottage is drawn up for 1 year. Payments are made monthly at 1 thousand rubles. Determine the present value of the lease payments at a 12% discount rate. n = 12 (number of periods - months).

4 function. Accumulation of a monetary unit for a period. As a result of using this function, the future value of a series of equal periodic payments or receipts is determined.

Task... Determine the amount that will be accumulated on an account that yields 12% per annum by the end of the 5th year, if 10 thousand rubles are deposited annually on the account.

5 function. Amortization contribution for a monetary unit.

This function is the reciprocal of the present value of a regular annuity.

Depreciation Is the process defined by this function and includes interest on the loan and the payment of the principal amount of the debt.

Task. Determine what the annual payments should be in order to repay the loan of 100,000 rubles by the end of the 7th year, issued at 15% per annum.


An annuity can be either an income (incoming cash flow) or a payment (outgoing cash flow) in relation to the investor. Therefore, this function can be used in the case of calculating the amount of an equal contribution to repay a loan with a known number of installments and a given interest rate. Such a loan is called self-depreciating loan.

6 function. Considers the fund allocation factor and is the inverse of the unit accumulation function over the period.

The following formula is used to determine the amount of the payment:

Task... Determine what payments should be in order to have 100,000 rubles on the account at a rate of 12% per annum by the end of the 5th year.

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