Calculation lgd for bank deposits deposits. Formula and calculation of a bank deposit with capitalization
Term interest capitalization is used when making a deposit and means that interest will be added to its body with the frequency specified in the conditions and in the future the interest rate will be charged not only on the client's funds themselves, but also on accrued income. The frequency of adding interest to a deposit may differ from bank to bank, but the most commonly used are daily, monthly, quarterly, annually.
An alternative is the condition when the accrued interest is transferred to the client's account or card, and he can use the money by withdrawing it from an ATM or receiving it at the bank's cash desk. Under the condition of capitalization, the income and the total value of the deposit become larger. Moreover, the shorter the frequency of interest accrual or the longer the term of the deposit, the greater the difference in income between deposits with and without capitalization.
Income on a deposit with interest capitalization in the general case can be represented by the following formula:
D \u003d B x (1 + P) \u003d T, where
D - income on the deposit;
B - the amount of the deposit;
P - interest rate for one period for which interest is charged;
T - the number of periods for which funds are placed.
As for the formulas for different accrual periods, we will consider them below.
Deposits with daily capitalization
Such conditions are usually used in deposits with short terms (from several days to a couple of months) and in this case the accrual formula will look like this:
D \u003d B x (1 + P / 365) ^ T, where
D - income on the deposit;
B - the amount of the deposit;
T is the term of the deposit in days.
For example, let's take two identical deposits in the amount of 100,000 rubles and an interest rate of 10% per annum, the term of placement of funds is 5 years. On a deposit without capitalization, we will receive an income equal to 50,000 rubles, and with capitalization - 61,051 rubles. As you can see, the difference was more than 11,000 rubles. In the case of quarterly interest, this difference will be even greater. Calculations for the example are presented in the table below:
day | without capitalization | with capitalization | ||
Money in deposit | accrued interest |
Money in deposit | accrued interest |
|
1 | 100 000,00 | 27,40 | 100 000,00 | 27,40 |
2 | 100 000,00 | 27,40 | 100 027,40 | 27,40 |
3 | 100 000,00 | 27,40 | 100 054,80 | 27,41 |
4 | 100 000,00 | 27,40 | 100 082,21 | 27,42 |
5 | 100 000,00 | 27,40 | 100 109,63 | 27,43 |
TOTAL | 137,00 | 137,06 |
As we can see from the example, there is a small, but still, benefit from using capitalization.
Monthly capitalization
In the case of monthly capitalization, the calculation formula will be as follows:
D \u003d B x (1 + P / 12) ^ T, where
D - income on the deposit;
B - the amount of the deposit;
P - annual interest rate on the deposit;
T is the term of the deposit in months.
Let's apply this formula to the previous example. You can see the calculation in the table below:
month | without capitalization | with capitalization | ||
Money in deposit | accrued interest |
Money in deposit | accrued interest |
|
1 | 100 000,00 | 833,33 | 100 000,00 | 833,33 |
2 | 100 000,00 | 833,33 | 100 833,33 | 840,28 |
3 | 100 000,00 | 833,33 | 101 673,61 | 847,28 |
4 | 100 000,00 | 833,33 | 102 520,89 | 854,34 |
5 | 100 000,00 | 833,33 | 103 375,23 | 861,46 |
TOTAL | 4 166,65 | 4 236,69 |
As you can see, in this case, the difference was already quite a tangible amount.
Quarterly capitalization
The formula for calculating income on a deposit with a quarterly capitalization will look like this:
D \u003d B x (1 + P / 4) ^ T, where
D - income on the deposit;
B - the amount of the deposit;
P - annual interest rate on the deposit;
T is the term of the deposit in quarters.
quarter | without capitalization | with capitalization | ||
Money in deposit | accrued interest |
Money in deposit | accrued interest |
|
1 | 100 000,00 | 2 500,00 | 100 000,00 | 2 500,00 |
2 | 100 000,00 | 2 500,00 | 102 500,00 | 2 562,50 |
3 | 100 000,00 | 2 500,00 | 105 062,50 | 2 626,56 |
4 | 100 000,00 | 2 500,00 | 107 689,06 | 2 692,23 |
5 | 100 000,00 | 2 500,00 | 110 381,29 | 2 759,53 |
TOTAL | 12 500,00 | 13 140,82 |
As we can see, the difference between a deposit with and without capitalization has already amounted to more than one thousand rubles.
Annual capitalization
For deposits with annual capitalization, the calculation formula will look the most simple:
D \u003d B x (1 + P) \u003d T, where
D - income on the deposit;
B - the amount of the deposit;
P - annual interest rate on the deposit;
T is the term of the deposit in years.
For example, let's take the same conditions for a deposit. Calculations for the example are presented in the table below:
year | without capitalization | with capitalization | ||
Money in deposit | accrued interest |
Money in deposit | accrued interest |
|
1 | 100 000 | 10 000 | 100 000 | 10 000 |
2 | 100 000 | 10 000 | 110 000 | 11 000 |
3 | 100 000 | 10 000 | 121 000 | 12 100 |
4 | 100 000 | 10 000 | 133 100 | 13 310 |
5 | 100 000 | 10 000 | 146 410 | 14 641 |
TOTAL | 50 000 | 61 051 |
At the same time, for five years the difference between the two deposits amounted to more than 11,000 rubles.
In addition to the periods of capitalization accruals discussed above, banks can offer others, for example, once every six months, once every 10, 20, 100, 200, 400 days. Here conditions are limited only by fantasy. bank employees responsible for deposit programs.
Pros and cons of capitalization
But with such a plus as increased income, deposits with capitalization have a certain minus. When transferring interest to a card, a bank client can use the money received at any time, while, subject to capitalization, all income remains in the bank until the last day and can only be taken at the end of the deposit agreement.
Capitalization calculation in Excel
On our website you can download a form for calculating a deposit with capitalization in Excel. By substituting your data there, you can see your income on the deposit. In addition, the form allows you to make a calculation, taking into account partial withdrawals and replenishment of the deposit.
The capitalization condition is quite serious when choosing a deposit, it determines what income will be received in the end, so it must be taken into account. To compare different investments, you can use our selection form, and to calculate the income on them - calculator. Also on the pages of our site you can view and select deposits with daily, monthly, quarterly and annual capitalization.
22.06.2017 0
Today, banks offer many services to the population, the most popular of which are lending and depositing. Policies regarding loans and deposits are largely controlled by the Central Bank of the Russian Federation, as well as legislative acts Russia. However, banks have the right to provide loans and place deposits on certain conditions, if this does not contradict the law.
According to statistics, every 10th Russian is a client of this or that bank. That is why the question of how the calculation is made is so important. annual interest on a loan or bank deposit. In most cases, interest refers to the size of the bet. Depends on the amount of the bet total amount overpayments on the loan, as well as the amount of the monthly payment.
Annual percentage of deposits: calculation according to the formula
First of all, consider bank deposits. The conditions are specified in the agreement at the time of opening a deposit account. Interest is charged on the deposited amount. This is a monetary reward that the bank pays to the depositor for the use of his money.
The Civil Code of the Russian Federation provides for the possibility of citizens to withdraw a deposit at any time, along with accrued interest.
All the nuances, conditions and requirements for the deposit are reflected in the agreement between the bank and the depositor. The calculation of annual interest is carried out in two ways:
Annual percentage of the loan: calculation by the formula
Today, the demand for loans is huge, but the popularity of a particular loan product depends on the annual interest rate. In turn, the amount of the monthly payment depends on the interest rate.
When considering the issue of calculating interest on a loan, it is necessary to familiarize yourself with the basic definitions and features of lending in Russian banking institutions.
The annual interest rate is sum of money, which the borrower undertakes to pay at the end of the year. However, interest is usually calculated on a monthly or daily basis if we are talking on short-term loans.
No matter how attractive the interest rate on a loan looks, it should be understood that loans are never issued free of charge. It does not matter what type of loan is taken: a mortgage, a consumer loan or a car loan, the bank will still be paid an amount more than they took. To calculate the amount monthly payments, you must divide the annual rate by 12. In some cases, the lender sets the daily interest rate.
Example: a loan is taken at 20% per annum. How much interest from the body of the loan is required to pay daily? We believe: 20% : 365 = 0,054% .
Before signing loan agreement recommended to carefully review your financial position and also make predictions for the future. Today average rate in Russian banks is approximately 14%, so the overpayment on the loan and monthly payments can be quite large. If the borrower is unable to repay the debt, this will lead to the imposition of penalties, lawsuits and loss of property.
It is also worth knowing that interest rates may vary depending on their condition.:
- constant - the rate does not change and is set for the entire loan repayment period;
- floating depends on many parameters, for example, on the exchange rate, inflation, refinancing rate, etc.;
- multilevel - the main criterion for the rate is the amount of the remaining debt.
Having become familiar with the basic concepts, you can proceed to the calculation of the interest rate on a loan. For this you need:
- Find out the balance at the time of settlement and the amount of debt. For example, the balance is 3000 rubles.
- Find out the cost of all elements of the loan by taking an extract from credit account: 30 rub.
Using the formula, divide 30 by 3000, you get 0.01. - We multiply the resulting value by 100. The result is a rate that regulates monthly payments: 0.01 x 100 = 1%.
To calculate the annual rate, you need to multiply 1% by 12 months: 1 x 12 = 12% per annum.
Mortgage loans are calculated much more difficult, because include many variables. For a correct calculation, the loan amount and interest rate will not be enough. It is better to use a calculator that will help you calculate the approximate rate and amount of monthly mortgage payments.
Calculation of annual interest on a loan. Online calculator (balance by month and overpayment amount)
For a detailed determination of the annual interest on the loan, the distribution of the balance of the loan body by month and year, as well as displaying information in the form of a graph or table, you can use the online calculator for calculating
Content
Happy holders of their own bank deposits could earn more on a bank investment if they did not neglect public information on how to calculate interest on a deposit. After evaluating the main parameter - the interest rate, you need to pay attention to other conditions on which capitalization depends. To do this, you need to understand the difference between simple% and complex ones and, using specific examples, familiarize yourself with the calculation of the income amount for various types of savings.
What is deposit interest
According to the classical definition of finance, interest refers to the profit (remuneration) accrued and paid to the investor for the use of his funds. The purposes of use can be investments or any other activity that provides for the temporary alienation of these funds in favor of the interested party. Credit institutions make accruals in accordance with the concluded agreements, using a simple and complex calculation method.
Simple
With simple accrual, the profitability of the deposit is determined through the calculation of% at a time for the entire period of the account or regularly with a frequency, for example, once a month. The amount of monthly profit made under this accrual scheme is accumulated on a special account, separately from the main body of the deposit without a refund. Simple % can be withdrawn at the end of each contract period.
Complex
When calculating compound interest when opening deposits, the investor's profit is formed by accruing% on the amount increased by adding to the current body of the deposit the percentage yield of the previous period (frequency of capitalization). At a fixed rate, compound interest is more profitable for the investor than simple interest. The disadvantage is that banks use restrictions in the deposit agreement when withdrawing. This carries risks. For example, while the client is waiting for the expiration of the contract, a surge in inflation can eat up the entire profitability of a deposit of any size.
How to calculate interest on a deposit using a simple formula
If you have an urgent need to manage your funds by opening an investment at a simple%, then it is best to calculate the yield yourself according to the simple interest calculation formula. In practice, you may encounter two types of bank savings by replenishment: replenished and non-replenished by balance. How to calculate the numbers for each type is described below.
With the payment of simple interest at the end of the contract
- S = (P x I x (T / K))/100;
- S is the amount of profit;
- P is the size of the attachment;
- indicator I - annual rate;
- T – period of placement (calculate in days);
- K is the number of days in the current year;
- suppose a citizen decides to invest money for 180 days at an annual rate of 12%, the amount of savings is 100,000 rubles, according to the above formula, the yield can be calculated as follows: (100,000 * 12 * (180/365)) / 100 \u003d 5,916 rubles.
Calculation of a deposit with capitalization
Sometimes circumstances allow you to get additional money that you would like to save and increase on a bank deposit. There is no need to open a new separate account. If there is a corresponding clause in the contract, you can add money to an existing deposit. To check the correctness of accrual with replenishment, use the formula that will help you calculate the amount of the deposit with capitalization:
- S = ((P x I x (T / K))/100) + ((P 1 x I x (T 1 / K))/100);
- where the first and each subsequent component differ from each other by the variables P and T (the size and term of placement of the main body of the account).
Suppose a citizen has invested money for 60 days at 12% per annum with the possibility of replenishment. The initial amount is 50,000 rubles. On the 20th day, a citizen replenishes the account by 10,000 rubles. It turns out that 50,000 rubles lay on the deposit for 19 days (T). From the 20th to the 60th day (20 days, T1), the body of the account was 60,000 rubles. The interest on the deposit must be calculated as follows: ((50,000*12*(19/365))/100+((60,000*12*(20/365))/100 = 312.33+394.52=706.85 rubles.
How to calculate income on a deposit with interest capitalization
Those who have encountered microcredit organizations (MFIs) in their lives know that these creditors like to charge their debtors every day with% on the balance, which inflates the amount of debt. Simple bank depositor cannot count on the same returns, but the profit from accruing by the bank for the amount to which the cost of% for past period(capitalization) is of particular interest. It is better to calculate the percentage of the deposit amount yourself. This requires mastery of complex calculation formulas.
Non-replenishable deposit
When evaluating a proposal credit institution and the size of the loan, implying a non-replenishable account with monthly capitalization of interest, you must use the compound% algorithm. If MFIs set the frequency - once a day, then banks start from three months and less often from one. If capitalization is made every quarter or month, the yield grows more significantly. Interest on deposits made at compound interest is calculated according to the basic formula:
- S = (P x I x (G / K)) / 100;
- S is the amount of profit;
- P is the size of the attachment;
- I - annual interest rate;
- G is the period after which the capital is replenished;
- K is the number of days in the current year.
Further, the received amount of profitability is added to the initial body of the deposit, and the resulting figure is again put into circulation. For example, a citizen invested 100,000 rubles for a period of 90 days at 10% per year. The capitalization period is 30 days. The calculation of annual interest on deposits in rubles will be as follows:
- The first month of interest calculation when the deposit is opened: (100,000*10*(30/365))/100=822.
- Second month: ((100,000+822)*10*(30/365))/100=829.
- Third month: ((100 822+829)*10*(30/365))/100=835.
Deposit with replenishment during the term of the contract
An investment contract with replenishment implies that after each separate period, a certain amount of funds is added to the initial investment. The partial complexity of the formula for calculating income led to the development of special online deposit calculators return on replenished savings. If it is important for you to know how to calculate income, then check out the formula:
- S = P add.*M / I*((1+I / M) M*n-1)+P*(1+ I / M) M*n;
- S is the amount of income;
- P - initial amount bank deposit;
- P add. – amount of replenishment;
- I - annual interest rate (in hundredths, that is, you need to divide by 100);
- M is the number of capitalization periods;
- n – deposit term (number of years);
- Suppose a citizen has deposited 100,000 rubles in a bank for one year. at 12%, he can afford to replenish savings for 4000 monthly, after the expiration of the contract, the bank will have to return the amount: 4000*12/0.12*((1+0.12/12)12*1-1)+100000 *(1+012/12)12*1=163,412.52 rubles.
How to calculate the income on a deposit, taking into account the effective rate
Often, when evaluating the profitability of savings, people pay attention to only one parameter - the advertised interest rate, written in huge type. At best, some citizens have an understanding that% can be added to the balance and create a more efficient accumulation than when accrued at the end of the entire term. This is a superficial understanding that leads to underestimation of its benefits.
What is the effective deposit rate
This term is used by professionals financial market who understand that the bank attracts the client not only with one figure of the nominal interest rate, but also with the possibility of capitalization of%, as well as bonuses for fulfilling the conditions. The cumulative high interest income, taking into account all the nuances, is called the effective rate. This setting is different from nominal rate prescribed in the contract. With a normal investment, % can be mechanically calculated, accrued and withdrawn at the end of the contract.
Almost every future investor has to face the task of choosing a deposit that will bring the highest return. The interest rate declared by the bank cannot serve as the only criterion for comparison. Let's highlight the factors that, one way or another, may affect the amount of actual income ...
A fairly typical situation is when several deposits are opened at the same time. In this case, it is interesting to know the total balance for today, in the following months and at the end of the term on all deposits.
Deposit calculator, which is an offline version and allows you to use the main functionality even when there is no Internet connection.
Description
Return on investment calculator
The deposit calculator will calculate the profitability of the deposit, taking into account replenishments, capitalization and withholding tax; will allow you to calculate the effective interest rate - a relative value with which you can compare the actual yield of various deposits with each other.
Deposit calculator with capitalization
The "capitalization" interest accrual mode allows you to calculate deposits with interest capitalization - such deposits, in which income in the form of interest accrued by the bank is added to the principal amount of the deposit. The subsequent accrual of interest occurs on an already increased amount, which makes them more profitable, especially with a long-term investment.
Deposit calculator with replenishment
In the parameters "deposit replenishment" and "partial withdrawals" can be specified as periodic payments in order to be able to evaluate future income from the replenished deposit, as well as one-time with a fixed date for a more accurate accounting of investments on an already opened deposit.
Interest calculator for deposits including tax
When calculating the amount of interest on a deposit, it is important to take tax into account. In case you are tax resident, i.e. stay in the territory of the Russian Federation for more than 182 days a year, indicate the appropriate taxation regime
Deposit Calculator Report in Excel
By pressing the export button, you not only have the opportunity to get a full report in Excel on your deposit, but later import the deposit parameters from it, which will significantly save your time on keeping track of your savings.
Currently, banks offer potential customers a large number of types of financial products for savings and capital accumulation. Interest capitalized deposits are an excellent alternative to term deposits.
Before moving on to practice, let's understand the terminology used. Under capitalization, it is customary to understand the special conditions for calculating interest. In such a banking product, they will be credited to the amount initially deposited into the account with the frequency established by the agreement. Typically, this happens once a month. In subsequent accruals, interest will be added not only to the amount of the deposit, but also to the previously accrued income.
Many people, before concluding an agreement with a bank, prefer to independently double-check the information on the terms of the deposit provided by the bank employee. In such a situation, they are interested in how to calculate the contribution with interest capitalization.
So, to calculate the capitalization of interest on a deposit, we can use the following formula.
, where
- Dv - the final profitability, which consists of the initially deposited amount and the interest accrued on it;
- C - the amount deposited by the client in the bank;
- Rp - the size of the annual interest rate under the contract;
- T is the period of placement of funds.
It is possible to calculate the final amount of the deposit using the general formula, but it will be convenient to do this only for deposits with annual interest capitalization. If the frequency of adding interest is more frequent, then this calculation will undergo some changes.
We have already said above that most often capitalization is monthly. At the same time, individual banking institutions can develop and offer on the market deposits in which the capitalization will have a different frequency. It can also be daily or quarterly.
Therefore, for the convenience of our readers, below we will place ready-made formulas for such calculations.
Formula for deposits with monthly capitalization
, where
- Dv - profitability;
- C is the amount;
- T - for how many months the deposit is open.
When making such calculations, it is necessary to take into account important aspect, without which you will not be able to get the correct result. Under the terms of all bank deposits, the interest rate is indicated as a number with a percent sign. For example, 8% or 10%. However, in the calculation we must bring them to the following form 0.08 and 0.1, respectively.
Let's now analyze the calculation of interest on a deposit with a monthly capitalization of specific example. Suppose we have a deposit with the following conditions.
- The amount deposited in the bank is 100,000 rubles.
- The annual interest rate is 8%.
- The deposit is open for 12 months.
Now let's calculate the real income that the investor will receive on this deposit at the end of the term.
Formula for deposits with daily capitalization
In this case, the calculation of interest will look like this:
, where
- Dv - the amount of income;
- C - the deposited amount;
- Рп - the size of the annual interest rate;
- T - for how many days the deposit is open.
Of course, when you make the necessary calculations, you will see that the difference between a deposit with capitalization and a term banking product is not too great. But still, she is. Therefore, by choosing the financial product in question, the investor will receive more income as a result.
Formula for deposits with quarterly capitalization
In this case, the calculation of interest will look like this:
, where
- Dv - profitability;
- C is the amount;
- Рп - the size of the annual interest rate;
- T - for how many quarters the deposit is open.
Attentive readers, of course, have already noticed a pattern: the less frequently interest is added to the deposit amount, the lower the final income.