For the temporary use of the depositor's funds, the bank is obliged to calculate remuneration on a monthly basis. In fact, this is done according to the terms of the agreement between the bank and the client. The calculation of interest is included in the maintenance of the account and is performed without the participation of the depositor. But the depositor can independently calculate the interest on his deposit. To do this, you will need to acquire some skills and knowledge.
What are the interest rates on bank deposits?
Interest is divided by default into simple and compound. And interest is calculated in two ways - according to a simple and complex formula. The second method includes several schemes that differ from each other in the variability of the calculation. What is the difference between simple interest and compound interest?
Simple
The peculiarity of this type of accrual is that the interest on the deposit is not added to the principal amount, they are sent to another account opened under the terms of the agreement. At the conclusion of the contract, the frequency of accruals is also approved - once a month, quarterly, half a year, a year or at the end of the deposit term.
All terms are indicated at the choice of the depositor.
Complex
The second option is used for deposits with capitalization. Interest is automatically added to the body of the deposit, and each subsequent time the profit is accrued on a new, already increased amount. Thus, both the deposit amount and the interest rate are regularly growing.
How to correctly calculate the interest on the deposit?
First you need to understand for yourself all the conditions for the deposit, in particular, the frequency of interest accrual (monthly, quarterly, etc.), the type of interest accrual (simple or complex). After that, you can arm yourself with a calculator and proceed to the calculations.
How to use calculators?
The easiest– use the deposit profitability calculator on the website of the bank where the client has opened or is going to open a deposit. For example, on the Sberbank website. In the top menu, find the "Invest and Earn" section, then - "Deposits". A page with all offers will open. By choosing one of the options, at the bottom of the page you can see an online calculator that makes it easy to calculate income for this type of deposit. It is enough to enter the amount, the annual rate (it is entered automatically in the calculator for each product), the term of the deposit and click "Calculate".
The resulting figure is divided by 100 and the number of days in a year. This is the return on investment.
Simple formula calculation
Interest accrual on deposits without capitalization with a simple formula:
S=(P*I*t:K):100.
Designations:
- S - accrued profit.
- P is the amount of the deposit.
- I - annual rate on the deposit.
- t – deposit term (number of days).
- K is the number of days in a year (365 days are always taken into account when calculating interest, even in a leap year).
If the client invested 50,000 rubles. for a year at 4.7%, his income will be 2350 rubles: (50,000 * 4.7 * 365): 100 = 2350.
Complex formula calculation
At the request of the client, interest on the deposit may not be charged to a separate account, but added to the body of the deposit. In this case, you need to calculate the yield according to another, more complex formula:
S = ((P * I * (t: K)):100) + ((P 1 * I * (t 1: K)):100).
The peculiarity of this formula is that the initial and subsequent components each time differ in the variables P (deposit size) and t (number of days on the deposit). So, let's take a replenished deposit for 50,000, the interest rate is 12%, the term is 60 days. If the depositor replenished the account on the 20th day by another 10 thousand rubles, it turns out that the initial deposit was on the account for 19 days (t). From the 20th day to the 60th, the amount is 60,000 rubles. So the profit will be calculated as follows:
((50,000*12*(19:365)):100+((60,000*12*(20:365)):100 = 312.33+394.52=706.85 rubles.
Calculation of deposits with capitalization
To calculate interest on deposits with capitalization, another formula applies:
S=(P*I*j:K):100.
- S - percentage.
- P is the amount of the deposit plus any additional amounts received from capitalization.
- I is the interest rate on the deposit.
- t is the number of days in the period of time for which capitalization is performed.
- K - days in a year (365 or 366).
Visually, it looks like this: a deposit is made with a capitalization, for example, for 100 thousand rubles at 11.5%. Deadline - three months - June, July and August. Profit for the first month will be 945 rubles. - (100000*11.5*30:365:100). Income is added to the initial deposit, and thus for the second month it will be calculated: 100945 * 11.5 * 31:365:100 = 985 rubles. There are also 31 days in August, respectively, the calculation is made: 101930 * 11.5 * 31: 365: 100 \u003d 995.5 rubles.
As you can see, the gradation of interest occurs monthly, and at the same interest rate, a deposit with capitalization is more profitable.
How to calculate income taking into account the effective rate?
Rates with a similar characteristic are applicable only for deposits with capitalization. Profitability increases along the chain:
- unpaid profit is added to the principal amount;
- the amount on the deposit increases;
- accordingly, higher interest is charged;
- growing income.
Effective interest rate- this is the calculation of the profit accrued to the amount of the initial deposit by the end of the deposit term. It can be calculated using the formula:
(P*S)*(365:d)*100.
P is the profit for the entire deposit period.
S - deposit amount.
d - term of the deposit.
Examples of calculations for deposits
Formulas only at first glance seem incomprehensible. Having understood the terms once, each depositor can independently regulate his account and calculate his profitability.
Several examples of calculations.
Deposit without capitalization with calculation according to a simple formula. Amount - 100 thousand rubles, term - 180 days, interest rate - 4.72, taking into account capitalization. Total: (100,000 * 4.72: 180: 365): 100 = 2466.05 rubles. We add income to the body of the deposit, we get 102466.05 rubles.
According to another scheme, compound interest income will be calculated. Each option involves the possibility of adding interest to the principal amount of the deposit. Then both the amount of the deposit and the procedure for accruing profit change. Here is an example calculation compound interest.
If the client deposited 100 thousand rubles at 12% per annum for a period of 1 year, chose 3 months (quarterly) as the frequency of interest calculation, then the calculation procedure will be as follows:
- The number of days in a quarter is divided by the number of days in a year. It turns out: 91:365=0.25.
- This value is multiplied by the deposit amount and the income rate.
- Further - the number is divided by 100 (%): 100,000 * 12 * 0.25: 100 \u003d 3000.
It remains to multiply the resulting number by the number of accruals and add the result to the initial deposit amount: 3000*4+100,000=112,000.
Another type is deposits with the possibility of replenishment. Example:
- Deposit in the amount of 300 thousand rubles, term - 12 months, rate - 12%.
- The frequency of accrual of profit is 1 time per quarter.
- Replenishment - 50 thousand rubles each. every 3 months.
In total, the total amount of replenishment will be (for 3 times) 150 thousand rubles. Interest in the 1st quarter: 300000*0.12*91:365=8975.34 rubles For the second quarter, the profitability, taking into account replenishment, will be: (300,000 + 50,000) * 0.12 * 91: 365 = 10,471 rubles. 23 kop. In the third quarter: (400,000 + 50,000) * 0.12 * 91: 365 = 13463.01 rubles. At the end of the 4th term expires, so it does not count. The total profit will total 44876.4 rubles.
What deposits are taxed?
Citizens pay taxes on all income. If interest is charged on a person's deposits, can this be considered taxable income? The Ministry of Finance regularly makes proposals on the taxation of household deposits, but so far to standard deposits individuals this does not apply. How much interest income is taxable?
In 2018, the tax-free deposit rate will remain unchanged. It corresponds to the formula "The key rate of the Central Bank + 5%". This means that with a key rate of 8.25%, introduced by the Central Bank at the beginning of the year to attract customers, the maximum income on deposits for which you do not have to pay tax is 13.25%. Profits above this value will be taxed. For information: if the key rate of the Central Bank is exceeded, the tax on deposits can reach up to 35%. However, it is unprofitable for the bank itself to exceed this threshold, because it will itself be forced to pay deductions to the Deposit Insurance Agency at an increased rate.
From simple to complex...
Why does a person bring his savings to the bank? Of course, to ensure their safety, and most importantly - to receive income. And here, knowledge of the formula for simple or compound interest, as well as the ability to make a preliminary calculation of interest on a deposit, will come in handy as never before. After all, forecasting interest on deposits or interest on loans is one of the components of a reasonable management of your finances. It is good to carry out such forecasting before signing contracts and making financial transactions, as well as during periods of the next accrual of interest and adding it to the deposit under an already executed deposit agreement.
To calculate interest on deposits (deposits), and loans too, the following formulas are used:
- simple interest formula,
- compound interest formula.
A fixed rate is when the interest rate set for a bank deposit is fixed in a deposit agreement and remains unchanged for the entire period of investment, i.e. fixed. This rate can change only at the time of automatic prolongation of the contract for a new term or in case of early termination of the contractual relationship and payment of interest for the actual investment term at the “on demand” rate, which is stipulated by the conditions.
A floating rate is when the interest rate initially set under the contract can change during the entire investment period. The conditions and procedure for changing rates are stipulated in the deposit agreement. Interest rates may change: in connection with changes in the refinancing rate, with changes in the exchange rate, with the transfer of the deposit amount to another category, and other factors.
To calculate interest using formulas, you need to know the parameters of investing funds in a deposit account, namely:
- the amount of the deposit (deposit),
- interest rate on the selected deposit (deposit),
- interest calculation cycles (daily, monthly, quarterly, etc.),
- period of placement of the deposit (deposit),
- sometimes the type of interest rate used is also required - fixed or floating.
Now let's look at the above standard interest formulas that are used to calculate interest on deposits (deposits).
Simple interest formula
The simple interest formula is used if the interest accrued on the deposit is added to the deposit only at the end of the deposit term or is not added at all, but is transferred to a separate account, i.e. calculation of simple interest does not provide for the capitalization of interest.
When choosing the type of deposit, you should pay attention to the procedure for calculating interest. When the amount of the deposit and the period of placement are significant, and the bank uses the simple interest formula, this leads to an underestimation of the amount of the depositor's interest income. The formula for simple interest on deposits looks like this:
Simple interest formula
Symbol meaning:
S - the amount of funds due to be returned to the depositor at the end of the deposit period. It consists of the initial amount of funds placed, plus accrued interest.
I - annual interest rate
P - the initial amount of funds attracted to the deposit
Simple interest formula
Symbol meaning:
Sp - the amount of interest (income).
I - annual interest rate
t - the number of days of accrual of interest on the attracted deposit
K - number of days in a calendar year (365 or 366)
P is the amount of funds attracted to the deposit.
I will give conditional examples of calculating simple interest and the amount of a bank deposit with simple interest:
Example 1 Assume that the bank has accepted a deposit in the amount of 50,000 rubles for a period of 30 days. Fixed interest rate - 10.5% per annum. Applying the formulas, we get the following results:
S = 50000 + 50000 * 10.5 * 30 / 365 / 100 = 50431.51
Sp = 50000 * 10.5 * 30 / 365 / 100 = 431.51
Example 2 The bank accepted a deposit in the same amount of 50,000 rubles for a period of 3 months (90 days) at a fixed rate of 10.5 percent "annual". Only the term of investment has changed in the conditions.
S = 50000 + 50000 * 10.5 * 90 / 365 / 100 = 51294.52
Sp = 50000 * 10.5 * 90 / 365 / 100 = 1294.52
When comparing the two examples, it can be seen that the amount of monthly accrued interest according to the simple interest formula does not change.
431.51 * 3 months = 1294.52 rubles.
Example 3 The bank accepted a deposit in the amount of 50,000 rubles for a period of 3 months (90 days) at a fixed rate of 10.5 percent "annual". The deposit is replenishable, and on the 61st day the deposit was replenished in the amount of 10,000 rubles.
S1 \u003d 50000 + 50000 * 10.5 * 60 / 365 / 100 \u003d 50863.01
Sp1 = 50000 * 10.5 * 60 / 365 / 100 = 863.01
S2 = 60000 + 60000 * 10.5 * 30 / 365 / 100 = 60517.81
Sp2 = 60000 * 10.5 * 30 / 365 / 100 = 517.81
Sp = Sp1 + Sp2 = 50000 * 10.5 * 60 / 365 / 100 + 60000 * 10.5 * 30 / 365 / 100 = 863.01 + 517.81 = 1380.82
Example 4 The bank accepted a deposit in the same amount of 50,000 rubles for a period of 3 months (90 days), at a floating rate. For the first month (30 days) the interest rate is 10.5%, for the next 2 months (60 days) the interest rate is 12%.
S1 = 50000 + 50000 * 10.5 * 30 / 365 / 100 = 50000 + 431.51 = 50431.51
Sp1 = 50000 * 10.5 * 30 / 365 / 100 = 431.51
S2 = 50000 + 50000 * 12 * 60 / 365 / 100 = 50000 + 986.3 = 50986.3
Sp2 = 50000 * 12 * 60 / 365 / 100 = 986.3
Sp = 50000 * 10.5 * 30 / 365 / 100 + 50000 * 12 * 60 / 365 / 100 = 431.51 + 986.3 = 1417.81
Compound interest formula
The compound interest formula is applied if the interest on the deposit is calculated at regular intervals (daily, monthly, quarterly) and the accrued interest is added to the deposit, i.e. the calculation of compound interest provides for the capitalization of interest (calculation of interest on interest).
Most banks offer deposits with quarterly capitalization (Sberbank of Russia, VTB, etc.), i.е. with compound interest. And some banks, in terms of deposits, offer capitalization at the end of the investment period, i.e. when the deposit is extended for the next term, which, to put it mildly, refers to a publicity stunt that encourages the depositor not to take the accrued interest, but the interest itself is actually calculated according to the simple interest formula. And I repeat, when the amount of the deposit and the period of placement are significant, such “capitalization” does not lead to an increase in the amount of the depositor’s interest income, because there is no accrual of interest on interest income received in previous periods.
The compound interest formula looks like this:
Compound interest formula
Symbol meaning:
S - the amount of funds due to be returned to the depositor at the end of the deposit term. It consists of the amount of the deposit (deposit) with interest.
Calculating only compound interest using a formula would look like this:
Calculation of compound interest only
Symbol meaning:
I - annual interest rate;
j is the number of calendar days in the period following which the bank capitalizes accrued interest;
K is the number of days in a calendar year (365 or 366);
P is the initial amount of funds attracted to the deposit;
n - the number of operations for the capitalization of accrued interest during the total period of attraction of funds;
Sp - the amount of interest (income).
I will give a conditional example of calculating compound interest and the amount of a bank deposit with compound interest:
Example 5 A deposit in the amount of 50 thousand rubles was accepted. for a period of 90 days at a fixed rate of 10.5 percent per annum. Interest is charged monthly. Consequently, the number of operations for the capitalization of accrued interest (p) within 90 days will be - 3. And the number of calendar days in the period following which the bank capitalizes accrued interest (j) will be - 30 days (90/3). What will be the amount of interest?
S \u003d 50000 * (1 + 10.5 * 30 / 365 / 100) 3 \u003d 51305.72
Sp = 50000 * (1 + 10.5 * 30 / 365 / 100)3 - 50000 = 1305.72
You can verify the correctness of the amount of interest calculated using the compound interest method by double-checking the calculation using the simple interest formula.
To do this, we divide the deposit period into 3 independent periods (3 months) of 30 days each and calculate the interest for each period using the simple interest formula. The amount of the deposit in each next period will be taken taking into account the interest for previous periods. As a result of the calculation, it turned out:
So, the total amount of interest, taking into account the monthly capitalization (calculation of interest on interest), is:
Sp = Sp1 + Sp2 + Sp3 = 431.51 + 435.23+ 438.98 = 1305.72
This corresponds to the amount calculated from compound interest in example 5.
And when calculating interest for the same period using the simple interest formula in example No. 2, the income amounted to only 1294.52 rubles. The capitalization of interest brought the depositor an additional 11.2 rubles. (1305.72 - 1294.52), i.e. higher yields are obtained from deposits with interest capitalization when compound interest is applied.
When calculating interest, one more small nuance must be taken into account. When determining the number of days for accruing interest on a deposit (t) or the number of calendar days in the period following which the bank capitalizes the accrued interest (j), the day of closing (withdrawal) of the deposit is not taken into account. So, for example, on November 2, 2007, the bank accepted a deposit for a period of 7 days. The full term of the deposit is from 02.11.07 to 09.11.07, i.е. 8 calendar days. And the period of accrual of interest on the deposit will be from 02.11.07 to 08.11.07, i.е. – 7 calendar days. Day 09.11.07 is not taken into account because the deposit is returned to the client.
Finishing the material, I want to once again draw your attention to the fact that according to the above interest formulas, you can also calculate interest on loans. Good luck with your income and expenses.
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 from it according to the existing tax rate the amount of the tax itself.
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, after 10 years on the specified conditions, the amount of the deposit, taking into account profit, will double, and net profit will amount to 1.0 million rubles.
compound interest income
Compound interest differs from simple interest in that it takes into account additional replenishment of the deposit amount with current income from investments, on which interest is also charged. 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 more high percentage return on the deposit, the total return 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.
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Bank deposit calculator for Android
We also offer absolutely free download of a bank deposit calculator - an application for Windows 10.Free deposit calculator for Windows 10
Calculation of the profitability of the deposit online.This deposit calculator calculates the deposit, taking into account deposits, withdrawals, the refinancing rate of the Central Bank, withholding tax, as well as the exchange rate - in the case of foreign currency deposits.
Calculation of the deposit with interest capitalization.
Capitalization on the deposit - adding the interest received to the amount of the deposit, followed by the accrual of income for the increased amount.
Setting the calculation parameters with interest capitalization will allow you to calculate the deposit when the accrued interest amount is added to the deposit amount and accrual in the new period occurs with a new amount of savings. Such investments are more profitable. Calculations of deposits with capitalization coincide with the calculations of deposits from such banks as Tinkoff and Sberbank, VTB.
Calculation of deposits allowing deposits and withdrawals
You can set the parameters for deposits and withdrawals, as well as the amount of the minimum balance on the deposit. The calculation will be made taking into account deposits and withdrawals and you will receive the resulting deposit amount.
A deposit with replenishment allows you to accumulate funds, for example, for a down payment on a mortgage. Saving money for a mortgage through a deposit is a fairly common way to buy an apartment. Many Russians resort to it.
The deposit calculator helps you understand how much money you will have at the end of the accumulation and how much you need to replenish in order to have enough for the initial deposit. Naturally, the deposit should be opened as much as possible with a maximum percentage and capitalization. Such investments are the most profitable and safe. Other ways to increase your money is to play on the stock exchange or invest in yourself. But these costs do not guarantee a 100% payback. The deposit is distinguished by stability, you always know that your money will return to you thanks to the deposit insurance system from the state. But this applies to deposits of less than 1400 thousand rubles.
Deposits and taxes
As previously stated, deposits above a certain rate are taxed. More precisely, income on the deposit or income in the amount is taxed = income at the rate in the contract - income at the rate of the Central Bank +5.
35 or 30 percent are taken from this income, depending on whether you are a resident or not.
Taxes must be accounted for by the bank. Although sometimes the bank does not write off taxes, and then sends a letter that you need to go to the tax office. Although the bank should do it. In this case, it is recommended to go to Personal Area taxpayer and see if you need to pay this tax. If you don't get it, then you probably won't have to pay. No need to waste your time. When calculating, the tax is rounded to an integer, i.e. everything less than 50 kopecks is rounded to zero, which is more than one. This should also be taken into account in the calculations.
Deposit and investment terms
Deposits can have investment terms from a week to 5 years. Although it may be higher. Although I had a deposit for 5 years.
Investing for the long term is an additional risk. For 5 years, money can depreciate. For a long time, you can take a chance and make a foreign currency deposit or pick up and open a metal account. Gold rises in price quite strongly and falls weakly.
Another option is to open a deposit in rubles and take out a mortgage. You pay the bank a fixed amount and you will have an apartment. When you still have money on deposit, you always know that even if the money depreciates, you will pay the bank a fixed amount, which can be taken from the deposit. It's simple - money will depreciate, your debt will depreciate. But this is if you have a loan in rubles. Everything is more complicated in the currency. When the ruble depreciates, the currency is more expensive and mortgage payments will increase. Taking a mortgage in foreign currency is an unjustified risk.
Deposit interest - this is the remuneration paid by the bank to the depositor for the temporary use of his in cash. As per requirement Central Bank RF, all credit organizations operating in Russia are required to calculate interest on deposits daily. Formally, this is what happens, but in fact the client receives interest under the terms of the contract. To understand how to calculate interest on a deposit, it should be borne in mind that banks use two methods for calculating them: simple and difficult (when contributing with ).
In the first case, interest is not added to the body of the deposit (invested amount), but transferred to another account of the depositor in accordance with the terms of the agreement. As a rule, accrual of income occurs monthly, quarterly, once every 6 months, once a year or at the end of the deposit term. In the second case, the accrued income is added to the body of the deposit within the terms stipulated by the agreement (more often monthly or quarterly). Since the principal amount of the deposit increases periodically, the interest accrued on it also increases. In the end, the total return on the deposit increases, and quite noticeably.
It turns out that with the same nominal interest rate, identical deposit amount and validity period, it brings more profitability. This must be taken into account when choosing the optimal offer.
Calculation of interest on a deposit with simple accrual
S = (P x I x t / K) / 100, where:
S - the amount of accrued interest
R - deposited amount
I - annual interest rate on the deposit
t — period for which interest will be calculated, in days
K - the number of days in a year (there is also a leap year)
Calculation example: Suppose that a client has made a deposit with a simple accrual in the amount of 100 thousand rubles for 1 year at 11.5% per annum. It turns out that when closing the deposit, the depositor will receive an income in the amount of: (100,000 x 11.5 x 365/365) / 100 = 11,500 rubles.
Calculation of interest on a deposit with capitalization
S = (P x I x j / K) / 100, where:
S - the amount of accrued interest
P - the deposited amount, as well as all subsequent amounts increased as a result of capitalization
I - annual interest on the deposit
j is the number of days in the period for which capitalization is made,
K - number of days in a year
Calculation example: Let's assume that the client made a deposit with a capitalization of 100 thousand rubles for 3 months (June, July, August) at 11.5% per annum.
Income for June will be: (100,000 x 11.5 x 30 / 365) / 100 = 945 rubles.
We add this amount to the 100,000 rubles of the deposit body in order to calculate the accrued interest for July: (100945 x 11.5 x 31 / 365) / 100 = 985 rubles.
Similarly, we calculate income for August: (101930 x 11.5 x 31/365) / 100 = 995.5 rubles.
As can be seen from the calculation, in August the return on the deposit is higher than in July, although each month has 31 days. This is due to the capitalization of interest.