Each depositor, placing a deposit in a bank, wants to know how much income can be received at the end of the term. Today there are two main ways of calculating interest: complex and simple, and each financial institution calculates profit in its own way. In the article, we will consider how to calculate the interest on a deposit.
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Interest calculation schemes are complex and simple, while simple circuit accrual lies in the fact that the interest is accrued either at the end of the contract term, or to a separate account, from which the client can withdraw it once a month or a quarter.
The second scheme involves the capitalization of interest, that is, the accrued interest is added to the deposit amount, increasing it. In the next period, interest income is calculated from the already increased deposit amount.
A complex scheme is more profitable because it allows you to get more income. However, the rates for such programs are lower.
Basic Formulas
Easy option
The formula for calculating the interest on the deposit must be written in the terms of the contract.
It looks like this:
, where:
Let's take an example. The depositor has deposited 10000 rubles. Annual rate - 10% per annum. The deposit program does not imply replenishment and capitalization.
According to the calculation this method we get:
Thus, for 3 months deposit, the client will receive interest in the amount 246.6 rubles.
Simple interest is also applicable in cases of replenished deposits. In this case, the calculation is carried out as follows.
Customer put 10000 rubles under 10% per annum, for a period of 3 months. The deposit was replenished twice 1000 rubles. The first is through 30 days, the second - in two months.
Thus, the client will receive 82.2 rubles in the first month before replenishment of the deposit, and 180.8 rubles And 295.9 rubles in the second and third periods, respectively.
Hard version
A complex method of calculation involves the capitalization of interest. Let's look at an example diagram. The client placed a deposit 100000 rubles at the rate 8,7% , for half a year. Deposit conditions - from. The calculation is made as follows.
S \u003d 100000 * (1 + 8.7 * 30 / 365/100) 6 - 100000 \u003d 4367.9 rubles.
At the end of the deposit period, the client will receive 4367.9 rubles additional profit. Checking the calculation is very simple using the simple interest formula. To do this, the term of the deposit is divided into separate periods and the balance is taken for calculation, taking into account previous payments and accruals.
| Month | Deposit amount | Interest rate | Amount of days | Interest amount | Deposit amount at the end of the period |
| 1 | 100000 | 8,7% | 30 days | 715,1 | 100715,1 |
| 2 | 100715,1 | 8,7% | 30 days | 720,18 | 101435,28 |
| 3 | 101435,28 | 8,7% | 30 days | 725,34 | 102160,62 |
| 4 | 102160,62 | 8,7% | 30 days | 730,52 | 102891,14 |
| 5 | 102891,14 | 8,7% | 30 days | 735,74 | 103626,88 |
| 6 | 103626,88 | 8,7% | 30 days | 741 | 104367,88 |
Thus, the table shows that the compound interest formula is easier to apply than the calculation of a contribution with capitalization using simple interest.
By substituting the values of deposits into the formulas, you can independently calculate the final income
For an account with deposits
Deposit programs with replenishment also have features for calculating interest.
The annual rate of such deposits is somewhat lower. This is explained by the fact that over the period of the agreement, the refinancing rate may decrease, and the deposit will become unprofitable for the bank.
Let us give an example of calculating interest on a deposit with replenishment.
The client opens a deposit in the amount 70000 rubles at the rate 7% per annum for 3 months.
For the first month, the income will be:
After replenishing the deposit on 3000 rubles, the account contains an amount of 73000 rubles.
Recalculation for the year:
Income for the remaining 60 days:
The total amount of interest on the deposit for three months will be 1242 rubles from the amount in 73000 rubles. And the final amount of the deposit 74242 rubles.
Important disclaimers about deposit interest calculations
Effective rate
Effective interest rate allows you to estimate the real income from a particular contribution. It is this rate that allows you to compare different offers from banks and choose the most profitable.
Since the capitalization of deposits significantly affects the income from the deposit, the effective rate is calculated using the following formula:
S effective = ((1+I/100/n) n – 1) x 100
, where:
Let's use an example to calculate. The deposit is placed in the bank for 1 year at 10% per annum. Interest capitalization - monthly.
S effective = ((1+10/100/12) 12 - 1) x 100 = 10.43%
In this case, the effective annual interest rate will be 10,43% .
That is, when choosing a deposit, it is necessary to compare the effective rates. Today there is enough online services for calculating deposit rates. Similar calculators can be found on the websites of banks.
Taxing
Any income of a citizen of the Russian Federation established by law is subject to tax. In the case of a bank, such income is the percentage of excess of the refinancing rate.
As of August 2019, the refinancing rate has not been set. From January 1, 2019 central bank Russian Federation decided not to single out refinancing as a separate rate, but to equate it to the key one.
The key rate in 2019 is 11% , which means that if the interest on the deposit is higher than this value, then such income must be subject to personal income tax - 35% .
Let's turn to the law. Information about taxes paid individuals from income, considers Article 214.2 of the Tax Code of the Russian Federation, as amended and supplemented as of the date of application. So, you can make simple calculations.
If the client places a deposit of 10,000 rubles for a period of 1 year at a simple interest rate of 12.3%, then upon the expiration of the contract, he will have to pay to the tax office:
- 10000 *12,3% = 1230 rubles;
- 10000*11% = 1100 rubles;
- (1230-1100)*35% = 45.5 rubles.
Thus, in this example, it can be seen that taxes will amount to 45.5 rubles. The bank is responsible for deducting taxes, and the client will simply receive a reduced amount in his hands.
Dependence on timing
The final income from the deposit depends on the terms and it is quite simple to calculate it manually.
With a deposit of 10,000 rubles at a rate of 8% per annum, we will calculate as follows:
- determine what the daily accrual is equal to 1% : 10000/100 = 100 rubles;
- multiply by the amount of interest that the bank gives: 100 * 8 \u003d 800 rubles;
- add the percentage to the body of the deposit: 10000 + 800 = 10800 rubles.
If the money is placed not for a year, but for another period, then it is more difficult to calculate the percentage. Consider the same example, but the term of the deposit will be 182 days.
The annual return will be 800 rubles. Behind 1 day year the investor will receive: 800/365 = 2,192 rubles. This is the value of the deposit accrued daily. The deposit conditions in the example state that the term is 182 days, respectively, it is necessary to multiply given term for daily income: 182 * 2.192 = 398.9 rubles.
In banks, the terms of deposits are indicated in months or years, but days are still used in the calculation.
So, the most common times are:
- 1 month - 30 days;
- 3 months - 90 days;
- six months - 182 days;
- year - 365 days.
With a replenished deposit, the process is more laborious. In this case, you can use the online calculator.
An example of how to check the total
When calculating on a calculator, an incorrect amount may be given, since the technical factor always exists. If the deposit was opened earlier and there is an account statement with all the accruals on hand, then it is very easy to check the correctness of the accrual of income.
For example, on February 20, a client opens a deposit with a quarterly capitalization. Deposit amount 10000 rubles, bid 10% . Term - 9 months or 272 days. took off on August 15 5000 rubles.
| days | date of | Coming | Consumption | Account amount |
| February 20, 2019 | 10000 | 0 | 5000 | |
| 49 | April 10, 2019 | 30000 | 0 | 35000 |
| 42 | May 20, 2019 | 535 | 0 | 35535 |
| 85 | August 15, 2019 | 0 | 5000 | 30535 |
| 6 | August 20, 2019 | 744,77 | 0 | 31324,95 |
| 91 | November 20, 2019 | 789,95 | 0 | 32027,83 |
- From February 20 to April 10: 10000*9/100*49/365 = 120.8.
- From April 10 to May 20: 40000*9/100*42/365 = 414.2.
- February 20 to May 20: 120.8 + 414.2 = 535.
- From May 20 to August 15: 35535 * 9/100 * 85/365 = 744.77.
- From August 15 to August 20: 30535 * 9/100 * 6/365 = 45.18.
- From May 20 to August 20: 744.77 + 45.18 = 789.95.
- From August 20 to November 20: 31324.95 * 9/100 * 91/365 = 702.88.
Most online calculators are used to automate relatively simple calculations that can be done manually. For example, the calculation of tax on income or sales actually involves two steps: determining the tax base and separating the amount of the tax itself from it at the existing tax rate.
The compound interest calculator is distinguished by the automatic calculation of the income that investments bring over a certain period. For clarity, consider the option of a bank deposit on the terms and compound interest.
simple interest income
For such deposits, profit is calculated based on the nominal amount of the deposit. Simply put, the percentage of profit is determined only from the amount that was originally placed on the deposit. At the same time, the amounts of income constantly arriving on interest are not taken into account.
The calculation of income in this case can be determined by the following formula:
BS = TS × (1 + PS × PV), where:
- PV is the investment time period in years.
Let the deposit amount be 1.0 million rubles at 10% per annum for a period of 10 years. Determine the amount that will be in the bank account at the end of the deposit term.
BS \u003d 1,000,000 × (1 + 0.1 × 10) \u003d 2,000,000 rubles.
That is, in 10 years, under the specified conditions, the amount of the deposit, taking into account the profit, will double, and the net profit will be 1.0 million rubles.
compound interest income
Compound interest is different from simple topics that it takes into account the additional replenishment of the deposit amount with current income from investments, which also accrue interest. The calculation formula looks like this:
BS \u003d TS × (1 + PS) PV, where:
- BS - the future amount, taking into account the income from investments;
- TS - initial deposit amount;
- PS - interest rate on the deposit;
- PV (degree) - investment time period in years.
Substituting the values from the simple percentage example, we get:
BS \u003d 1,000,000 × (1 + 0.1) 10 \u003d 2,590,000 rubles.
Thus, after 10 years, the net profit on compound interest will be 1,590,000 rubles, which is 590 thousand rubles higher than the profit on simple interest.
A situation may arise when, with a higher percentage of return on the deposit, the total profit on investments for the same period will be lower due to the simple interest on the deposit. In this case, using both calculators, you should calculate both deposit options and choose the more profitable one. Do not forget to take into account the fact that deposits with compound interest before the end of the term do not imply withdrawal of interest in the form of income. Thus, as a result, your income will be higher, but you will be able to receive it only after the end of the entire period specified in the contract.
Compound interest is the effect of adding percentage of profits to the principal amount of an investment. In this way interest creates new profit. Using the compound interest formula, you can calculate the amount taking into account the calculation of interest.
Calculating compound interest
For example, you have a bank deposit of 100,000 rubles at 10% per annum. After 12 months, you will have 100,000 + 100,000 × 10% = 110,000 rubles in your account. That is, the profit will be 10,000 rubles. If you leave 110,000 rubles. for another year with the same conditions, then in another 12 months the account will accumulate 110,000 + 110,000 × 10% = 121,000 rubles. The profit of the first year will be added to the main contribution and will participate in the formation of income. For the third, fourth and subsequent years, the profit will be formed in the same way, constantly increasing.
Compound interest formula:
∑ = Y × (1 + %)n
- ∑ – total;
- Y is the original amount;
- % - interest rate;
- n is the number of periods (years, months, quarters).
Example
You opened an account for five years by depositing 5,000 rubles in the bank. with 10% per annum. What will be the amount after 5 years? Substitute the numbers in the formula:
∑ \u003d 5,000 × (1 + 10 / 100) × 5 \u003d 8,052.5 rubles.
Compound interest is used when opening term deposits. The contract specifies the frequency of accrual: every quarter, month, year.
Example
If an account of 10,000 rubles is opened. for a year at 10% with monthly accrual.
∑ \u003d 10,000 × (1 + 10 / 100 / 12) × 12 \u003d 11,047.13 rubles.
11,047.13 − 10,000 = 1,047.13 rubles
Profit per year:
1 047,13 / 10 000 = 10,47 %
With this scheme, the yield is higher than with a one-time (annual) accrual. If you do not withdraw profits, you will earn compound interest.
Formula for bank deposit
Compound interest for a bank deposit is a little more difficult to calculate than described above. The interest rate is calculated by the formula:
- p - interest rate (annual interest / 100). At a rate of 10.5%, the interest rate would be 10.5 / 100 = 0.105.
- d is the number of days in which interest will be calculated. With monthly capitalization is 30 days. With quarterly - 90 days.
- y - days of the calendar year (365 or 366).
Compound interest for bank deposits calculated by the formula:
X×(1+p×d/y)n
The attractiveness of compound interest lies in the avalanche-like increase in the contribution. At first, the increase is small, but over time it becomes very noticeable.
Example
Contribution - 50,000 rubles. Term - 15 years.
- Simple interest: Conditions - 20% without additional contributions and with regular profit withdrawals. With the amount of the deposit will increase every year by 10,000 rubles, and in 15 years will be 200,000 rubles.
- Compound interest: Conditions - 20% without additional contributions, but interest is added annually to the original deposit amount. After one year, the results will be the same as with simple interest, but after 2 years the difference will be 2,000 rubles, after 3 years - 6,400 rubles. etc. After 15 years, a contribution from 50,000 rubles. will increase to 770,351 rubles.
Compound interest is especially beneficial for long-term investments. With simple interest, profit increases linearly, since regular withdrawals do not allow it to work for the deposit. Profit will create profit only with compound interest, the effect is especially noticeable with a good interest rate and a long-term deposit. If the annual interest rate is 10%, after 15 years 50,000 rubles. will become 200,000, at 15% - 400,000, at 20% - 780,000. You can verify the correctness of the calculations using our calculator.
The online deposit calculator will help you quickly calculate the interest on any deposit, including those with capitalization, with replenishment and taxes, and will also show the interest calculation schedule. If you are planning to open a deposit, then the calculator will help you calculate the potential profitability in advance.
Interest capitalization
With an ordinary deposit, the bank pays the accrued interest to the depositor on a monthly basis (or at other intervals specified in the terms of the agreement). This is called "simple interest". Deposit with capitalization (or " compound interest”) is a condition under which accrued interest is not paid, but is added to the deposit amount, thus increasing it. The total income from the deposit in this case will be higher.
Using the deposit calculator, you can compare the calculation results of two identical deposits (with and without capitalization) and see the difference.
Effective interest rate on the deposit
This characteristic is relevant only for deposits with interest capitalization. Due to the fact that interest is not paid but is used to increase the amount of the deposit, it is obvious that if the amount of the deposit increases every month, then the newly accrued interest on this amount will also be higher, as well as the final income.
Formula for calculating the effective rate:
where
N - the number of interest payments during the term of the deposit,
T - term of deposit placement in months.
This formula is not universal. It is suitable only for deposits with capitalization once a month, the period of which contains an integer number of months. For other deposits (for example, a deposit for 100 days), this formula will not work.
However, there is a universal formula for calculating the effective rate. The disadvantage of this formula is that you can get the result only after calculating the interest on the deposit.
Effective rate = (P / S) * (365 / d) * 100
where
P - interest accrued for the entire period of the deposit,
S - deposit amount,
d - term of the deposit in days.
This formula is suitable for all deposits, with any terms and any periodicity of capitalization. She simply considers the ratio of income received to the initial amount of the contribution, bringing this value to annual interest. Only a small error can be present here if the deposit period or part of it fell on a leap year.
It is this method that is used to calculate the effective rate in the deposit calculator presented here.
Income tax on deposits
The Tax Code of the Russian Federation provides for the taxation of deposits in the following cases:
- If the interest rate on the ruble deposit exceeds the value of the key rate of the Central Bank of the Russian Federation at the time of conclusion or prolongation of the agreement, increased by 5 percentage points.
- If the interest rate on a foreign currency deposit exceeds 9% .
The tax rate is 35% for Russian residents and 30% for non-residents.
At the same time, not all income received from the deposit is taxed, but only a part received as a result of exceeding the interest rate on the deposit of the threshold rate. In order to calculate tax base(the taxable amount), you must first calculate the interest accrued at the nominal rate of the deposit, and then make a similar calculation at the threshold rate. The difference between these amounts will be the tax base. To get the amount of tax, it remains to multiply this amount by the tax rate.
Our deposit calculator will calculate your deposit including taxes.
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 calculation or the longer the term of the deposit, the more difference in income between deposits with and without capitalization.
Income on a deposit with capitalization of interest in 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 formulas different periods accruals, 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 calculation 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 placement period Money- 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, the conditions are limited only by the imagination of 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 up to last day remains in the bank and can be taken only 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.
