6 5 percent per annum. We calculate simple interest. Object requirement
It is quite clear that the meaning of a bank deposit is to receive income in the form of interest. How can this income be calculated in advance?
The simplest case is a deposit for a year without replenishment
If the deposit is issued exactly for a year with interest at the end of the term, it is very easy to determine the amount of payments. Let's say a deposit in the amount of 700,000 rubles was opened on July 15, 2014 for 1 year at 9 percent per annum. So, on July 15, 2015, the investor will receive his 700 thousand plus income:
700,000 x 9: 100 = 63,000 rubles.
Deposit for a period of less or more than a year without replenishment
If the same 700,000 rubles are deposited at the same 9% per annum, but for 180 days, or 6 months, the calculation will be a little more complicated:
700,000 x 9 / 100 / 365 (or 366) x 180 = 31068.50
where 365 or 366 is the number of days in a particular year.
Deposit with replenishment
Let's complicate the task and assume that a deposit is opened with the possibility of replenishment. Conditions: a deposit in the amount of 500,000 rubles was issued on July 15, 2014 for a period of 1 year at the same 9% per annum. On December 10, the deposit was replenished by 200,000 rubles. Question: what income will the depositor receive on July 15, 2015?
500,000 rubles lay for 148 days;
700,000 rubles lay for 217 days.
We add 148 and 217 for verification, we get 365 - which means that the days are calculated correctly.
500,000 x 9 / 100 / 365 x 148 \u003d 18,246.58 rubles.
700,000 x 9 / 100 / 365 x 217 \u003d 37,454.79 rubles.
Total amount of income: 18246.58 + 37454.79 = 55701.37 rubles.
The most difficult case is a deposit with capitalization
Capitalization in banking is the addition of interest received to the initial amount of the deposit. Consider another example: the same 700,000 rubles are deposited for 1 year (365 days) at 9% per annum, with monthly interest. This interest can either be withdrawn monthly or capitalized. It is intuitively clear that with the same percentage, the income in the second case will be greater. Let's count.
Income for the first month: 700,000x9 / 100 / 365x30 = 5178.08 (30 - the number of days in a month, maybe 31, in February 28 or 29).
We add the received interest to the deposit amount and calculate the income for the second month:
(700,000+5178.08)х9/100/365*30=5216.39
Third month:
(700,000+5,178.08+5,216.39)x9/100/365x30=5254.97
And so on. If we conditionally assume that there are 30 days in each month, then the income for the year will be 64,728.4 rubles. It is cumbersome to count in this way, but the result will be accurate, especially if we start from the actual number of days in each month.
It should also be borne in mind: the interest on a deposit with capitalization is usually lower than without it. It makes sense not only to consult with a bank employee, but also independently calculate and compare the profitability of different deposits. It may turn out that it is more profitable to put funds on a deposit without capitalization, but at a higher percentage.
Greetings! I am sure that I do not have to know and be able to do everything in the world. Yes, this is impossible in principle. But in the most important areas for a person, it is worth navigating at least at the level of a “teapot”.
I include work, business, family, health and, of course, money as vital areas. What am I leading to? To the fact that any investment requires. Even if it is a banal bank deposit or business development loan.
To be honest, I have not done such calculations manually for a very long time. For what? After all, there are a lot of convenient applications and online calculators. As a last resort, a “fail-safe” Excel spreadsheet will help out.
But it doesn’t hurt to know the elementary formulas for basic calculations! Agree, interest on deposits or loans can definitely be attributed to the "basic".
Below we will recall school algebra. It must come in handy somewhere in life.
We calculate the percentage of the deposit amount
Let me remind you that interest on a bank deposit can be simple and complex.
In the first case, the bank accrues income on the initial amount of the deposit. That is, every month / quarter / year the depositor receives the same “bonus” from the bank.
Of course, the calculation formulas for simple and compound interest are different from each other.
Let's consider them on a concrete example.
Return on investment with simple interest
- Amount % \u003d (deposit * rate * days in the billing period) / (days in the year * 100)
Example. Valera opened a deposit in the amount of 20,000 rubles at 9% per annum for one year.
Calculate the return on investment for a year, a month, a week and one day.
The amount of interest for the year \u003d (20,000 * 9 * 365) / (365 * 100) \u003d 1800 rubles
It is clear that in our example, the annual yield could be calculated much easier: 20,000 * 0.09. And as a result, get the same 1800 rubles. But since we decided to count according to the formula, then we will count according to it. The main thing is to understand the logic.
The amount of interest for the month (June) \u003d (20,000 * 9 * 30) / (365 * 100) \u003d 148 rubles
The amount of interest for the week \u003d (20,000 * 9 * 7) / (365 * 100) \u003d 34.5 rubles
The amount of interest per day = (20,000 * 9 * 1) / (365 * 100) = 5 rubles
Agree, the formula of simple interest is elementary. It allows you to calculate the return on the deposit for any number of days.
Return on investment with compound interest
Let's complicate the example. The formula for calculating compound interest is a little more “tricky” than in the previous version. The calculator must have a "degree" function. Alternatively, you can use the degree option in an Excel spreadsheet.
- Amount % = contribution * (1 + rate for the capitalization period) number of capitalizations - contribution
- Rate for the capitalization period = (annual rate*days in the capitalization period)/(number of days in a year*100)
Let's go back to our example. Valera placed the same 20,000 rubles on a bank deposit at 9% per annum. But this time - .
First, let's calculate the rate for the capitalization period. According to the terms of the deposit, interest is accrued and "plus" to the deposit once a month. This means that we have 30 days in the capitalization period.
Thus, the rate for the capitalization period = (9*30)/(365*100) = 0.0074%
And now we consider how much our contribution will bring in the form of interest for different periods.
The amount of interest for the year \u003d 20,000 * (1 + 0.0074) 12 - 20,000 \u003d 1,850 rubles
We raise to the power of "12" because the year includes twelve periods of capitalization.
As you can see, even with such a symbolic amount and a short term, the difference in the yield of a deposit with simple and compound interest is 50 rubles.
The amount of interest for six months \u003d 20,000 * (1 + 0.0074) 6 - 20,000 \u003d 905 rubles
The amount of interest for the quarter \u003d 20,000 * (1 + 0.0074) 3 - 20,000 \u003d 447 rubles
The amount of interest for the month = 20,000 * (1 + 0.0074) 1 - 20,000 = 148 rubles
Note! Capitalization of interest does not affect the profitability of the deposit for the first month.
The depositor will receive all the same 148 rubles with both simple and compound interest. Differences in yields will start from the second month. And the longer the term of the deposit, the more significant the difference will be.
Before we get too far away from the topic of compound interest, let's check how true one of the recommendations of financial consultants is. I mean the advice to choose not once every six months or a quarter, but once a month.
Suppose our conditional Valera made a deposit for the same amount, term and at the same rate, but with capitalization of interest every six months.
Rate = (9*182)/(365*100) = 0.0449%
Now we calculate the return on investment for the year.
The amount of interest for the year \u003d 20,000 * (1 + 0.0449) 2 - 20,000 \u003d 1,836 rubles
Conclusion: other things being equal, the semi-annual capitalization will bring Valera 14 rubles less than the monthly one (1850 - 1836).
I understand that the difference is very small. But after all, other initial data we have are symbolic. On large sums and long terms, 14 rubles will turn into thousands and millions.
We calculate the percentage of the loan
We are moving from deposits to loans. In fact, the formula for calculating a loan is no different from the basic one.
Example. Yuri took out a consumer loan at Sberbank in the amount of 100,000 rubles for 2 years at 20% per annum.
- Amount % \u003d (balance of debt * annual rate * days in the billing period) / (number of days in a year * 100)
The amount of interest for the first month = (100000 * 20 * 30) / (365 * 100) = 1644 rubles
The amount of interest for one day \u003d (100000 * 20 * 1) / (365 * 100) \u003d 55 rubles
Note! Along with the balance of the debt, the amount of interest on the loan also decreases. In this regard, the differentiated scheme is much more "fair" than the annuity one.
Now let's say our Yuri paid off half of his loan. And now the balance of his debt to the bank is not 100,000, but 50,000 rubles.
How much will the interest burden be reduced for him?
The amount of interest per month = (50,000 * 20 * 30) / (365 * 100) = 822 rubles (instead of 1644)
The amount of interest for one day \u003d (50,000 * 20 * 1) / (365 * 100) \u003d 27 rubles (instead of 55)
Everything is fair: the debt to the bank has halved - the “interest” burden on the borrower has halved.
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Deposit interest - this is the remuneration paid by the bank to the depositor for the temporary use of his funds. According to the requirement of the Central Bank of the Russian Federation, all credit institutions 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 term of the deposit. 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: Assume that a client has 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.
The banking system in the modern world is an indispensable element of the economy of any country, while exerting a significant impact on other areas of society. Credit institutions provide the population with numerous services that are aimed at ensuring the optimal life of each individual.
The greatest demand is for loans and deposits. They are regulated both by the policy of the bank and by the laws of the country. The terms of provision depend on many reasons, affecting the demand of each user.
Therefore, sooner or later, a bank client becomes interested in calculating the annual interest on his deposit or loan. The very definition of "interest" depends on the type of contract with the organization, but the essence is the same - the financial well-being of the user of bank services depends on the size of the rate. For this reason, many are concerned about the question “how to calculate the annual percentage?”.
Annual percentage of deposits: calculation
First of all, it is worth paying attention to the following section of the functions carried out by the bank - deposits. The organization accepts from a person a certain amount of money for a specified period or without it at all. At the same time, the Civil Code establishes that when a client requests a return, the organization is obliged to pay the amount with interest.
It is this condition that encourages people to open deposits. Interest on a deposit is a monetary reward paid by a credit institution for the right to temporarily use the client's funds.
The size, conditions and requirements for such a process are reflected in the terms of the contract. It is clear that the depositor will choose the institution in which the interest rate on the deposit will be higher. But at the same time, the bank should not remain in the red.
I.Simple. When using this method, interest is not added to the deposit amount, but is transferred to the client's account in accordance with the agreement. At the same time, remuneration can be accrued every month, quarter, every six months, a year, or only at the end of the deposit term.
The calculation is quite simple and can be done independently. To do this, use the following formula:
S = (P x I x t / K) / 100%.
The indicators are decoded as follows:
- R - the amount of the contribution in monetary units;
- I
- t – term of the deposit;
- K is the number of whole days in a year.
Example: a client entered into an agreement to open a deposit in the amount of 300 thousand rubles for a period of 12 months with an annual rate of 10%. At the end of the deposit, he will receive: 30,000 rubles \u003d (300,000 x 10 x 365/365) / 100%
II.Complex or deposit with capitalization. The remuneration is accrued immediately to the invested amount once a month or quarter. This contributes to an increase in the body of the deposit and, as a result, interest on it. Thus, the size of the subsequent profit increases and takes on quite tangible values.
This method has its own calculation formula, which looks like:
S = (P x I x j / K) / 100.
Wherein:
- R – initial and subsequent deposit amounts;
- I - interest rate per year on the deposit;
- j – term of capitalization;
- K is the number of whole days in a year.
Example: a client entered into an agreement for the amount of 300 thousand rubles for a period of 3 months with an annual rate of 10%.
The income for the first month will be equal to: 2465 rubles \u003d (300,000 x 10 x 30/365) / 100.
In the same way, the third month: 2506 rubles \u003d (304951 x 10 x 30/365) / 100.
You can see that every month the profitability is getting higher. This pattern is explained by the capitalization of interest.
It turns out that with identical interest rates, the same deposit size and validity period, a deposit with capitalization will bring more profit than with simple interest. This should be taken into account when choosing the most effective option.
Annual loan interest: calculation
Having dealt with deposits, it is worth considering another segment of banking services - lending. This is the main function of such financial institutions. The demand for a product of this kind largely depends on the annual interest rate. It determines the amount of money that the client pays at the specified time to the organization for the right to use borrowed money.
Before answering the question “how to calculate interest per annum?”, You need to familiarize yourself with the basic concepts and nuances of lending to financial organizations:
- Before taking out a loan you need to carefully analyze your current and future financial condition, since the average rate in the country's banks is at the level of 14%. Overpayments can form large enough amounts, as a result of which a situation of impossibility of repaying the debt may occur, which ultimately can lead to numerous losses.
- A credit card has entered the everyday life of the country's population quite quickly and easily, as it is very convenient and beneficial to use. Its feature is as follows: Interest will not accrue if the spent amount is repaid within the specified period.
- Rates may vary according to their condition. There are three types:
- constant - t what value remains unchanged for the entire period of repayment of the loan;
- floating - h depends on many factors, so it can change at least every day;
- multilevel - The main criterion that determines the amount of the rate is the amount of debt.
So, having familiarized yourself with the main nuances of the interest rate in lending, you can go directly to its calculation.
Initially, it is worth dealing with the annual interest on a credit card. For a complete understanding of the actions taken, the discussion will proceed in accordance with the example. So, to do this operation, you need to follow the steps:
- Check the current balance, as well as the amount of debt. The balance is 3 thousand rubles.
- Set the cost of all components of the loan. To do this, you need to refer to the latest bank statement: 30 rubles.
- Divide the set amount by the amount of debt: 30/3000=0.01.
- The resulting number must be multiplied by 100. You get the interest rate that regulates payments for the month: 0.01 x 100 \u003d 1%.
- To calculate the interest rate for the year, you need to multiply the answer by 12: 1% x 12 \u003d 12%
The calculation of interest on a credit card is quite simple and does not require special programs and consultants.
But things are different with mortgages:
- Mortgage loans in terms of the calculation structure are quite complex, as they include many variables, therefore it will not be possible to be satisfied with knowing only the amount of the loan and the interest rate for the year.
- Besides, each bank may use different calculation methods than other organizations. Therefore, on almost every website of a financial institution there is a specialized calculator that allows you to make calculations in accordance with the conditions put forward by the organization. This feature helps to analyze a wide range of banks and choose the best lending option.
- It is worth paying special attention to the implicit payments that pop up when calculating the interest rate on a mortgage. The creditor may hide some details of the contract and evade their disclosure. In this case, it is highly recommended not to enter into any agreements with such banks. In order not to get into an unpleasant situation, you need to have all the data on the loan that are available to the borrower.
The annual interest rate and its calculation depend on many factors: starting from the policy pursued by the bank and ending with the state of the economy in the country. It should be understood that its size is affected not only by financial indicators, but also by relations between states. Especially if it concerns deposits and loans that were concluded in foreign currency.
With such parameters, no one can assume an absolutely correct outcome in the effectiveness of one of the options. Such processes will always be accompanied by risk. But to reduce it, it is necessary to analyze the proposals of banks, study their reputation, conditions and requirements.
Hello dear readers!
Recently, we had a very serious elderly lady in the office. The late husband left her a substantial amount earned from his own business. Grandmother asked how she could calculate the interest on her own. Oh, if all old people were so attentive! Most of them, unfortunately, easily give away their last savings to scammers. I taught my grandmother. Be in the know too.
The more investment, the more profit. You don't have to do anything yourself.
Opening a deposit in a bank is a passive type of income that is gaining popularity among the inhabitants of our country. Its popularity is simply explainable: you invest “free” money in a bank, wait a certain period of time and make a profit.
Of course, a bank consultant, for example, Sberbank, will be happy to tell you what is written in his booklet about banking offers: such and such a deposit, yield - up to 10 percent per annum, etc.
But what is this 10 percent? You brought real money, and they tell you about some abstract interest. Surely, you want to know what these percentages mean in terms of real money, what will be your profit in rubles after one month, a year? Not every bank employee will be able to provide you with such information.
But you can calculate everything yourself. Calculations only seem to be complicated. In fact, everything is simple, they are made according to the calculation formula. This formula changes depending on the capitalization of interest: if it is, one calculation algorithm is needed, if it is not, another. However, even if you do not have a calculator at hand, you can use the formula to accurately determine the return on investment.
Calculate simple interest
The formula works when interest capitalization is not expected. In other words, you deposit money into an account and leave it there for a period of time.
During this period, there is no change in the interest rate and the amount of the deposit.
Let's say the deposit is 200,000 rubles. The annual interest rate is 10 percent. How to calculate the profit that the investment will give?
Let's apply the following formula:
S = (P × I × t ÷ K) ÷ 100
Symbol S the amount of accrued interest that we must receive in order to find out the profit is indicated.
P- the amount we put into the account.
I- annual interest rate.
t– the period (days) for which interest is calculated (usually, about half of the deposit term).
K- the number of days in a year (365 or 366 if the year is a leap year).
Let's count:
S = 200,000 × 10 × 184 ÷ 365 ÷ 100 = 10082 (rubles). We have received the amount of interest that will be accrued for 184 days.
Calculating compound interest
When is compound interest required? If the capitalization of the contribution is expected.
Capitalization of the deposit - this means that the interest that is accrued per month must be added to the amount of your investment.
Thus, for the second month, to calculate the interest, you should take the initial amount of the deposit, plus the interest accrued in the first month.
S = (P × I × j ÷ K) ÷ 100
S- profit (accrued interest for a certain period).
P- the amount deposited to the account initially, taking into account capitalization in subsequent months.
I- annual percentage.
J– days during which capitalization takes place.
K- the number of days in a year.
First, let's calculate what the deposit amount will be after a month.
200,000 × 10 × 30 ÷ 365 ÷ 100 = 1643 (rubles) - interest that will be accrued per month. We add them to 200,000 rubles. To calculate the interest for the second month, we take as P the amount of 201,643 rubles.
The calculation of profit for the second month, if it has 31 days, will be as follows:
201 643 × 10 × 31 ÷ 365 ÷ 100 = 1712 (rubles).
If this formula is applied to each month, we will see how profit grows during the year.
Be careful!
Calculate the compound interest rate
Compound (effective) interest rate on the deposit shows how much income the depositor actually has. It turns out after carrying out operations with compound interest. This is the amount of interest for the entire period of the bank's work with your deposit. The rate is calculated by the bank in order to inform potential depositors about the benefits of cooperation with a particular bank.
The effective interest rate is also determined when it comes to credit. To calculate it, the borrower needs to calculate the entire amount of the debt, i.e. add the amount that the bank issued to him with the cost of the loan (interest), commissions for certain services (for example, SMS alerts, etc.), the amount of loan insurance, etc. After receiving this amount, you can calculate how much the contribution will need to be made monthly.
It is not easy to determine the effective interest rate on your own. Banks that have an online version have calculators with which the compound interest rate is calculated very quickly.
About the procedure for calculating interest on a video deposit:
How to calculate the percentage of a specific amount?
What is the algorithm for calculating the percentage of a certain amount? Let's turn to mathematics, remembering how we calculated the percentage of the number in the lessons.
For example, you need to determine how much 60% of 1000 rubles will be.
Reasoning options:
- First way. We take 1000 rubles for 100 percent. We need to find X (60 percent of the amount in rubles). X - 60 percent. So, X \u003d 1000 × 60% ÷ 100% \u003d 600 rubles. We received 60 percent of 1,000 rubles, which is 600 rubles.
- The second, easier way. 60 percent is 0.3 of the amount. Therefore, to find 60 percent of 1000 rubles, you can multiply 0.3 by 1000. It turns out 600 (rubles). The calculation is much shorter, but no less accurate than the first one.
Let's solve a couple more simple examples to find simple percentages:
How much in rubles will be 18 percent per annum from a deposit of 20,000 rubles?
0.18 × 20,000 = 3,600 rubles for one year.
Let's calculate 19 percent per annum for 2 years (24 months). The total interest is 8000. The task is to find out what the initial amount of the deposit was.
Imagine that you are taking an exam and you come across such a task
Let's figure it out. We deposited a certain amount into the account. Let's denote it, as before, P. 19 percent of profit is accrued per year. The term of the deposit is 24 months. During this time, we were the happy owners of an additional 8,000 rubles. So, P × 0.19 × 2 = 8000 (we multiplied the start-up capital by the annual percentage and by the number of years).
P = 8000 ÷ 0, 19 ÷ 2 = 21,052 (rubles) - this was our contribution to the bank.
Let's work with another example.
500,000 - the amount deposited in a bank account at 10 percent per annum. The term of the deposit is 10 years.
We decide. 500,000 × 0.1 × 10 = 500,000 rubles percent. Those. in 10 years, our sum at an annual interest of 10 should double, and we will receive 1,000,000 rubles.
Let's calculate percentages using examples
The loan amount is 20,000 rubles. The annual percentage is 18.9%. Simple percentage.
What will be the monthly payment?
20,000 × 0.189 = 3780 is the interest for the year. Per month, the interest will be 12 times less than this amount. So, it will be 315 rubles. Divide 20,000 by 12 (the number of months in a year). We get 1667 rubles. This is the share of the principal debt attributable to one month. We add to it 315 rubles. Total, 1982 rubles - a monthly loan payment.
What contribution should be made today in a business that gives 15 percent of profit per year, so that after 24 months there will be 300,000 rubles?
Let's start with the fact that after 24 months we will have 300,000 rubles (this is the amount of our investment with interest on the deposit for 2 years).
We deposited a certain amount (P) into the bank account. Annual percentage - 15.
Therefore, 2 × P × 0.15 + P = 300,000 rubles. P \u003d 300,000 ÷ (0, 3 + 1) \u003d 230,769 rubles is our initial investment.
The amount of 5000 rubles is put in the bank. The annual percentage is 7.8%. What will I receive at the end of the year?
We calculate: 5000 × 0.078 + 5000 = 5390 rubles.
And if you open a deposit in the amount of 50,000 rubles with an annual percentage of 7.6 for a period of 99 days?
In our country, the English method of interest is recognized, so it is considered that there are 365 days in a year. So, 50,000 × 0.076 × 99 ÷ 365 = 1030 rubles - interest for the specified period of time (99 days). At the output, the amount will be 51,030 rubles.
From 15,000 rubles, you need to subtract 20 percent. Let's denote 15,000 as 100 percent. 0.2 is the share of 20 percent in total. Subtract 0.2 × 15,000 from 15,000 to get 12,000.
Let's do one more calculation.
How much will 5% of the amount of 60,000,000 rubles be in rubles? 0.05 × 60,000,000 = 3,000,000 rubles.
Now let's determine what the daily interest will be if the annual is 17.9?
We argue as follows: for the whole year, the amount we initially deposited is on the account, giving us a profit of 17.9 percent at the end of the year. How much profit does this amount give per month? 17.9 ÷ 12 = 1.49 percent - profit every month. And on the day? 17.9 ÷ 365 = 0.049 percent added daily to our deposit.
For example, the deposit amount is 100,000 rubles. The percentage of profit per year is 17.8. The annual amount of interest will be equal to 0.178 × 100,000 = 17,800 rubles (per year). The daily amount of interest is calculated by dividing the annual amount by 365. We get 48 rubles - daily profit.
Finally, we calculate 5% of the amount of 2000.
Everything is extremely simple. 2000 x 0.05 = 100.
We calculate the interest on the deposit without the help of a bank consultant
It is clear to everyone that deposits in a bank are made for profit. And profit is interest. How can you immediately determine the profit?
Annual deposit without replenishment
When making an annual deposit, when it is supposed to receive interest at the end of the year, it is not difficult to calculate the profit.
Suppose 700 thousand rubles are deposited in the account. The contribution was made on 07/15/2014. The term of the deposit is one year. Interest rate - 9%. Consequently, on July 15, 2015, the investor returned his 700,000 rubles and received 63,000 profits in addition to them (the calculation is as follows: 700,000 × 9 ÷ 100 = 63,000).
Deposit for a period of more or less than a year without replenishment
Let's say 700 thousand rubles are deposited in a bank account, as in the previous case. But the term of the deposit is 180 days. The annual percentage is still 9%.
The calculation in this case will be more complicated:
700,000 must be multiplied by 9, divided by 9, then by 100 and then by 365. It turns out 172.603. We multiply this number by 180. The result is 31,068.5.
Deposit with replenishment
Let's make the task even more difficult.
Let's say that we have opened a deposit that we can replenish as much as possible. The deposit (500,000 rubles) was opened on July 15, 2016 on the following terms: annual interest - 9%, deposit term - one year. On December 10, 2016, we replenished the account by depositing another 200 thousand rubles. The question is, what profit will we get on July 15, 2017, i.e. after closing the deposit?
First, let's calculate how many days passed from 07/15/2016 to 07/09/2016 (the period when the deposit was 500 thousand rubles), and then how many days the deposit was 700 thousand rubles (from 12/10/2016 to 07/14/2017).
It turns out:
500 thousand rubles were on the account for 148 days;
700 thousand rubles - within 217 days.
We add 148 to 217. The sum is 365. So, we have calculated everything correctly.
We multiply 500,000 by 9, divide the product of these numbers by 100, divide the resulting amount by 365 and multiply by 148. Total - 18,246 rubles 58 kopecks (income for the first period).
We multiply 700,000 by 9, divide the product of these numbers by 100, divide the resulting sum by 365 and multiply by 217.
Total - 37,454 rubles 79 kopecks (income for the period after account replenishment).
We summarize the income for 2 periods: 18,246 rubles 58 kopecks + 37,454 rubles 79 kopecks = 55,701 rubles 37 kopecks.
Complex profit calculations taking into account capitalization
Capitalization of the deposit - determination of interest in each subsequent month based on the amount of the previous month with the interest accrued in this month added to it.
Let's say the contribution already known to us - 700 thousand rubles - was made for a year. Annual percentage - 9%. Interest is calculated every month. The investor has the right to withdraw interest on a monthly basis or to capitalize his contribution. The second case assumes a higher yield.
Let's do the calculation.
In the first month of banking, provided that it has 30 days, the deposit will increase by 5,178 rubles 8 kopecks (700,000 × 9 ÷ 100 ÷ 365 × 30 = 5,178.08).
We add this number to 700,000. It turns out 705,178.08 rubles. We multiply the sum by 9, divide by 100, then by 365 and multiply by 30. It turns out the number 5,216.39, i.e. 5 216 rubles 39 kopecks. Let's compare it with the result of the previous calculation. The difference is 38 rubles 31 kopecks.
Let's calculate the income for the third month:
700 000 + 5 178,08 + 5 216,39 = 710394,47.
710394, 47 multiply by 9, divide by 100, then by 365 and multiply by 30.
Total - 5254.97, i.e. 5254 rubles 97 kopecks.
Such a profit will give a deposit for three months. Similarly, income is calculated for 5, for 10, etc. months. The annual yield will be 64,728 rubles 4 kopecks, if we assume that the number of days in a month is 30.
Keep in mind that the annual interest on a deposit without capitalization is usually higher than on a deposit with capitalization.
Before choosing a deposit, find out all the details about the calculation of interest. Do the calculations yourself, compare the profitability of different deposits.
Investing without capitalization can bring you more profit than investing with it. And vice versa.
Calculation of profit when accrual of interest is carried out at the end of the deposit term
Investment for several years
The depositor opened a bank account for 10,000 rubles. The annual percentage is 9%. The investment period is 24 months.
For one year:
Let's take 10,000 as 100 percent. X is the number of rubles corresponding to 9%. X \u003d 10000 × 9 ÷ 100 \u003d 900. Profit for the first year - 900 rubles.
For 2 years:
The calculation is simple: multiply 900 by 2.
We receive 1800 rubles of profit from a two-year contribution.
Investment for several months
10,000 deposited in the account for 3 months. Annual percentage - 9%. For the year, the profit would be 900 rubles. Profit after 90 days - X.
X \u003d 900 × 90 ÷ 365 \u003d 221.92 rubles.
How to calculate the income from a replenished deposit, provided that the interest is paid at the end of the term?
Accounts that can be funded tend to offer lower returns. While the agreement is in effect, a decrease in the refinancing rate may occur, and the deposit of the depositor will not benefit the bank. Those. payments on the deposit will begin to exceed the interest paid by debtors who have taken out loans. However, this does not apply to situations where the deposit rate does not depend on the refinancing rate.
So, the refinancing rate rises - the interest rate on the deposit increases; the refinancing rate goes down - the investor's profit becomes less.
Deposit - 10,000 rubles. The term is 90 days. Annual percentage - 9%. After 30 days, the depositor deposited 3 thousand rubles into the account.
900 rubles - profit for the year, if the deposit had not been replenished.
For a month: 900 × 30 ÷ 365 = 73.972 rubles.
On the account after 30 days - 13 thousand rubles.
Recalculation for the whole year: 13000 × 9 ÷ 100 = 1170 rubles.
For the last 2 months: 1170 × 60 ÷ 365 = 192.33 rubles.
As a result, profit (all accrued interest): 266.302 rubles.
Calculation of income from a deposit with capitalization
The payment of interest on the deposit can be:
- one-time, i.e. on the day when the deposit agreement is signed, terminated or terminated;
- periodic: the amount is divided and issued every month, every three months, once a quarter or annually.
The choice is up to the client which of the following options to prefer:
- visit the bank at the intervals specified in the agreement in order to withdraw interest accrued over the past period;
- or receive them on the card automatically.
To capitalize interest means to add it to the balance of the deposit every month.
Imagine that you come to the bank every month on the day when interest is accrued, withdraw it and replenish your deposit with the withdrawn amount.
There is an increase in the balance of the deposit - interest is accrued on interest. Such deposits are recommended for people who do not plan to withdraw savings before the end of the deposit period.
There are deposits with the possible withdrawal of capitalized interest.
Calculate interest on a deposit with capitalization
On the first day of the year, a deposit was opened, involving the capitalization of interest. The deposit amount is 10,000 rubles. Annual percentage - 9%. The term is six months, i.e. 180 days. Interest is accrued and capitalized on the 30th or 31st of every month.
10000 × (1 + 0.09 × 30 ÷ 365) 3 × (1 + 0.09 × 28 ÷ 365) × (1 + 0.09 × 31 ÷ 365) 2 = 10000 × 1.007397260273973 3 × 1.00690410959 × 0.0076438356164384 2 = 10452.12 (rubles).
- 30 days - 3 months;
- 28 days - 1 month;
- 31 days - 2 months.
When calculating the number of days in a period, it must be borne in mind that when the last day of the period is a weekend, the end of the period is postponed to the first working day after it.
Because of this, online calculators cannot give a 100% accurate calculation. It is impossible to accurately calculate the interest on a deposit for 24 months if the approval of the production calendar is an annual matter.
Checking if the interest on the deposit is calculated correctly
Technology doesn't always work well. Having on hand an extract from the account, you can recalculate the interest that is due to be paid.
For example, on January 20, a contribution was made, 10,000 rubles. Interest is expected to be capitalized quarterly. The term of placement of funds is 273 days. Annual percentage - 9%. In March, on the 10th, there was a replenishment of the deposit by 30 thousand rubles. On July 15, the depositor withdrew 10 thousand rubles from the account. The 20th in April and the 20th in July are days off.
Art. 214.2 (TC RF) says that if at the conclusion of an agreement or its extension to three years, the interest on a deposit in rubles was higher in February 2014 than the refinancing rate by 5%, on interest income exceeding this value, the depositor must pay tax in at a rate of 35 percent. In this case, the bank must issue documents.
The procedure for calculating interest on a bank deposit in Excel:
How to calculate the profitability of the deposit yourself?
Many citizens of our country give their funds for storage and increase to banks. If the deposit does not exceed 700 thousand rubles, it is insured by the state. By opening a bank account, a person receives a guarantee of the return of his funds with interest added to them.
It is believed that the interest rate shows the profitability of the deposit. Is this opinion correct? Not true. It is necessary to take into account all the properties of the contribution in order to determine the profitability from it.
To predict profitability, you need to know how interest is calculated.
Working in a bank for a long time, I realized that most citizens do not know how to calculate interest. However, not all banks have conscientious employees. Many of them, just like clients, cannot calculate the profit from the deposit. That is why it is important to learn how to calculate the profitability of the deposit yourself.
200 thousand rubles were placed for a year.
Recall that there are 3 types of deposits:
- with the addition of profit to the deposit amount once a month;
- with accrual of profit once a quarter;
- with accrual of profit once a year.
2 formulas are used:
- to calculate simple interest;
- to calculate compound interest.
Simple interest means that the profit from the deposit is accrued before the expiration of the deposit. Compound interest is due to the addition of interest to the deposit amount on certain days.
Simple interest is calculated as follows:
S = (P x I x t ÷ K) ÷ 100 (S - profit; I - annual %; t - number of days on which interest on the deposit was calculated; K - days in a year; P - initial amount on the account).
Formula for calculating compound interest:
S = (P x I x j ÷ K) ÷ 100 (j is the number of days in the period at the end of which interest is capitalized; P is the amount of the deposit with accrued interest; S is the initial amount of the deposit with the addition of interest).
Example of interest capitalization once a month
The compound interest formula is used. In January, S = 1189.04 rubles (100,000 x 14 x 31 ÷ 365) ÷ 100 = 1189.04).
Add the amount of interest for the month to the original amount.
The result is 101,189.04 rubles.
In February, S = 1086.74 rubles (101,189.04 x 14 x 28 ÷ 356) ÷ 100 = 1086.74).
January interest is higher than February, because January has more days. Add 101189.04 to 1086.74. We get 102275.78 rubles. So for each month of contribution.
Example of interest capitalization once a quarter
There is a risk of making such a mistake (as my experience shows, it is common): to put in the formula instead of j = 90 or 91 days j = 30 or 31, i.e. take into account the number of days in one month, not in a quarter.
The calculation is made using the compound interest formula.
In the first quarter, S = 3452.05 rubles (100,000 x 14 x 90 ÷ 365) ÷ 100).
In the second quarter, instead of 100,000, we take 103452.05. Further, I hope everything is clear.
An example of capitalization at the end of the deposit period
We need a formula to calculate simple interest.
If the deposit is 100,000 rubles, S will be 14,000 rubles (100,000 x 14 x 365 ÷ 365) ÷ 100 = 14,000).
This is where the wisdom ends.
Calculate interest, carefully study the contract with the bank before signing it.
Be financially literate!
Multiply your money!
