Under interest funds should be understood the absolute size of the profit received as a result of the provision of money. They can be transmitted in any form. These can be various financial transactions. For example, a loan is issued, funds are deposited on a deposit account, products are sold on credit, a savings certificate, bonds, bills of exchange and so on are acquired. Of particular importance is the relationship between the rate of increase and the discount rate. Let's consider these elements in more detail.
Specificity
The interest rate is the relative amount of profit received for a certain (fixed) time period. It is formed by the ratio of income to debt. Its measurement is carried out in ordinary or decimal fraction or in percent. When analyzing financial transactions, specialists use this relative amount as an indicator of the degree of efficiency (profitability) of any commercial, economic, investment, and credit activity. It will not matter if there was a fact of investing funds and a process of increasing their volume, or it did not take place. The time period to which the interest rate is confined is called the accrual period. It can be a year, quarter, half year, month, or even day in some cases. As a rule, annual amounts are used in practice.
Logic of operations of discounting (increasing) capital
By agreement between the borrower and the lender, interest is paid as they accrue, or they are included in the principal amount of the debt. The increase in funds over time due to accession is the accumulation of capital. It is also called the growth of the amount. The discount rate is the reciprocal of the rate of increase. This is due to the fact that upon reduction, the amount that relates to the upcoming period is reduced by an indicator of the corresponding discount. In such cases, they say that discount (discounted) rates apply. The interest earned on them is called antisipative, and those that arose on the amount of increase are called destructive. This is the logic of capital discounting operations.
Accrual Features
In most cases, decursive percentages are simply called percentages. For their accrual a constant base is used. When it is taken as the amount that was received at the previous stage of reduction or increase, compound interest is applied. The increase and discounting in such cases takes place according to certain schemes. Relative amounts may be fixed. In this case, their size is determined in the contract. They can also be floating. In this case, the contract does not indicate the rate, but the base, which changes in the time period, as well as the amount of the premium - margin. The size of the latter is determined by the loan term, solvency of the borrower and other conditions. During the entire period of the loan operation, it can be variable or constant. In case of successive repayment of the debt, two options for calculating interest are allowed. In the first case, the interest rate (complex or simple) is applied to the actually existing amount of debt. The second option is used for consumer lending. In this case, the accrual is made for the entire amount of the obligation without taking into account its subsequent repayment. In practice, discrete amounts are used. They are charged for certain time periods (six months, a year, etc.). Build-up and discounting operations can be carried out continuously, for infinitely small periods. In this case, appropriate percentages (continuous) are also applied.
Build and discount formulas
An increased amount of debt (loan, deposit, other loans or invested funds) should be understood as the initial amount of money with interest at the end of the accrual period. Thus, we can denote:
- interest for the entire term - I;
- the initial amount of debt - P;
- increased amount of funds (at the end of the period) - S;
- interest rate - i;
- loan time - n.
For the entire period, interest will be:
I = Pni.
The increase in the amount is determined by the addition of initial funds and interest:
P + I = P + Pni = P (1+ ni) = S.
In practice, specialists often have to face the opposite task. From the amount S, which is payable after some time period n, you need to determine the size of the loan that was received - R. In such cases, there is a discount. The calculation is carried out when the interest on the amount of S will be held forward, directly when issuing a loan. The process of calculating interest and writing off it is called accounting. Interest itself is called a discount or a discount. To calculate, we need to use the equality S = P (1 + ni). It turns out P = S / (1 + ni). Thus, P will be the current size S paid after n years. The above calculations show simple types of discounting (accrual). In the latter case, the option of mathematical determination of the sum is considered. As you can see, the calculations use indicators that are used in the operations of growth and discounting.
Period duration
Accumulation and discounting operations can be calculated on two time bases. If K is 360 days, then commercial or ordinary interest is obtained. When applying the actual duration of a calendar year of 365 or 366 days, exact interest is calculated. The number of loan days is taken accurately and approximately. In the latter case, the month will be 30 days. The exact number of days can be determined by calculating their number between the dates when the loan was issued and when it should be repaid. According to Art. 839, paragraph 1 of the Civil Code, the days on which the deposit was opened and closed are not included in the total period for accrual.
Options Used
In practice, there are three methods for calculating interest:
- Exact amounts with a specific number of days. In this case, the designations AST / AST or 365/365 are used. This option is used by central and large commercial banking institutions in the United States and Great Britain. This method of calculation allows you to get the most accurate amounts.
- Normal interest with the exact number of loan days. In this case, the designations AST / 360 or 365/360 are used. This method is sometimes called banking. It is used in operations between banks of different countries or one state. This method, in particular, is common in Switzerland, Belgium, and France. With this calculation, a slightly larger amount is obtained than with the application of exact percentages.
- Normal interest with an approximate number of days (360/360). This method is practiced in commercial banks in Denmark, Germany, Sweden. This option is used in cases where the exact result is not needed (for example, in intermediate calculations).
In the process of investing in a short-term deposit, in some cases, a repeated sequential repetition of the increase in simple interest within the general specified period is used. Thus, reinvestment of the amounts received at each stage of increasing the volume of funds using a variable or a constant base is performed.
Abbreviation
Discounting can be considered as the definition of any value indicator relating to the upcoming time for an earlier period. Such a method is called reducing the value to a certain, usually initial, moment. The amount P obtained by reduction is called the current value or the current size of the future payment. Depending on the type of interest rate used, two discount options are used:
- The mathematical method.
- Commercial (banking) accounting.
In the first option, discussed above, the resulting fraction is called the discount factor. It reflects the share of the initial amount of debt in the final amount. When using the method of commercial accounting, a financial institution buys it from the owner at the cost less than indicated on paper before the due date for payment of a bill or other payment obligation. Thus, the acquisition is subject to discounts. Upon maturity, the bank, having received the money, realizes interest income in the form of a discount. The owner of the paper with the help of accounting has the opportunity to receive funds earlier than the period specified in it.
Features of a bill
This security is presented in the form of a debt receipt. A bill is drawn up in accordance with legal requirements. The rules provide for special forms in which the name, date of payment, the place where it is to be made, information about the subject to whom the payment is intended, information on the date and place of preparation of the paper, and the signature of the drawer are presented. Such promissory notes can be transferable and simple. The latter are presented in the form of documents that certify the unconditional financial obligation of the drawer to pay a certain amount to the holder of the paper upon maturity of the obligation. A transfer is a document issued by a borrower. A draft is a form of a special order to the direct payer (a banking organization, as a rule) on payment of a certain amount to a bill holder (third party) in a timely manner.
Accounting bills
For such securities, the commercial (banking) method is used. In accordance with it, interest on the use of a loan in the form of a discount will be charged on the amount that must be paid at the end of the period. The accounting indicator in this case is d. The size of the amount will be equal to Snd. N will be measured in years if d is the annual rate. The calculations will be as follows:
P = S - Snd = S (1 - nd), where n is the period from the moment of accounting to the day of repayment of the obligation;
(1 - nd) - discount factor.
Accounting, as a rule, is carried out with a temporary base K equal to 360 days, the number of loan days is most often taken accurate.
Other options
The increment and discount operations are calculated not only by simple interest. For example, the amounts are not paid immediately after accrual, but are included in the amount owed. Such a connection is called interest capitalization. When calculating, you can apply the same indicators that were used above.
At the end of the first year, percentages are equal to Pi. The accumulated amount in this case will be P + Pi = P (1 + i). By the end of the second year, it will become P (1 + i) + P (1 + i) i = P (1 + i) 2 and so on. At the end of the year n, the sum will be S = P (1 + i) n, and the interest for this period I = S - P = P [(1 + i) n - 1].
(1 + i) n is the compounding multiplier by compound interest. Time in such cases is measured as AST / AST. Often the period for calculating interest is not an integer.
Interest accrual for increasing funds
The following accrual options for accrual:
- The calculation is carried out using an integer number of years. It is taken from the compound interest formula. The fractional part of the period is taken from the ratio of simple percent.
- According to the rules of some commercial banks, for a number of operations, the interest amount is calculated only for whole numbers of periods (years or other periods).
To compare the results of the increase in different percentages, it will be enough to compare the corresponding factors. With equal interest rates, the ratios of these indicators will substantially depend on the period. For n> 1 with extension, the difference will increase. When working with compound interest, rule 72 is used: if the interest rate is i, then the amount will be doubled in approximately 72 / i years. For example, at 12%, this will happen after 6 years.
Nominal and effective indicator
In modern conditions, interest capitalization is carried out, as a rule, not once, but several times during the year. This can be done on a quarterly or semi-annual basis. Some foreign commercial banking institutions also practice daily accrual. If we take j at the annual rate, the number of periods in a year is m, each time interest will be determined by j / m. The rate j is called nominal. There is also a valid (effective) indicator. It represents the annual compound interest rate. Using it, you get the same result as when applying m - a one-time interest calculation on j / m. This rate measures the relative real income that is obtained as a whole for the year.
