In recent years, the annuity method of repayment has become widespread in Russian market consumer lending. The peculiarity of this calculation method is that all payments have the same (equal) value, and the distribution of the amount of each payment between the loan body and accrued interest is different. In the first half of the settlement period, most of the payment is directed to the repayment of interest, in the second half the ratio is equalized and only in the last third of the period the payment distribution shifts in favor of the loan body.

The annuity payment is calculated based on the annuity coefficient of the following type:

K - annuity coefficient;
i – interest rate for one period;
n is the number of periods.

This is a classic calculation formula and each bank uses its own method of dividing repayment periods into periods (in days or months), so the results of calculations at the same rate may differ slightly.

The amount of payment for the annuity method of repayment depends on the calculated annuity ratio (K) and the size of the loan body and is determined as follows:

TC - the body of the loan (disbursed amount).
AP - annuity payment.

Next, we bring our mathematical formulas to a practical form. Since the interest rate is annual, and the loan is repaid monthly, i.e. 12 times a year, the formula for calculating the annuity payment takes the following form:

k - the number of months during which the loan is expected to be repaid.

As we said earlier, the amount of the annuity payment is distributed to repay the loan body and accrued interest. Since interest is calculated monthly on the balance of the loan debt, the formula for calculating it is as follows:

SZ - the amount of debt on the loan at the time of calculation
SP - the amount of interest accrued per month

Thus, the repayment of the loan body accounts for a part of the annuity payment amount, reduced by the amount of accrued interest.

Usually banks use exactly 12 months as a time base, however, some financial institutions make calculations based on the number of days in a year rather than months (usually 365 days): then the result is more accurate.

WITH practical application This technique can be seen in the following examples:

• an example of calculating annuity payments for the Sberbank Educational Loan received to pay for the Skolkovo MBA training program. Comparison with differentiated repayment method;
• an example of calculating interest and repayment schedule for a Sberbank consumer loan provided without collateral. The example considers annuity and differentiated repayment methods.

The loan is issued on the terms of further return of funds to the bank. Moreover, along with the repayment of the debt, the borrower must pay the interest rate. Despite the significance of the last parameter, the method of calculating payments is no less important in determining the level of overpayment. You should understand what is the difference between different forms of loan repayment and how to calculate the annuity loan payment.

Loan repayment

In 2016, the total amount of the population's loan debt exceeded 10,000 billion rubles. Most banking organizations negotiate the conditions for the return of borrowed funds before issuing them. There are two main forms of loan repayment:

• differentiated payments;
• annuity payments.

Although most borrowers, when choosing credit program focuses on the size of the interest rate and, based on this parameter, selects the optimal loan, the method of calculating interest and repaying the loan also plays a large role in its final cost.

Differentiated payments are more beneficial for the borrower. In the case of this method of returning funds, the client simultaneously repays both the "body" of the loan and the interest rate. Due to this, monthly payments will decrease every month, since every month interest is charged on a smaller amount (the loan body decreases with each subsequent payment).

For obvious reasons, this form of calculation has a number of positive features. First, the client immediately begins to pay the body of the loan. Secondly, at the same time there is a repayment of the interest rate. Thirdly, due to the gradual reduction of debt precisely by the body of the loan, and not by interest, the final cost of such a loan is lower than in the case of annuity loans. But since banking organizations are interested in obtaining the highest possible income, most often they use an annuity payment schedule.

Annuity payments

In the case of differentiated payments, the borrower immediately begins to repay the body of the loan. The less money the client owes to the bank, the lower the interest rate is. This is unprofitable for a financial institution, since it is the funds that come from paying interest that are the main source of income for such organizations. In the case of annuity payments, the situation looks different.

An annuity loan involves the repayment of debt in equal installments (which is not the case with a differentiated loan). A positive feature of this form of payments is the possibility of making a monthly fixed amount of a small amount. With a differentiated loan, the client needs to deposit more money right away, but over time, loan payments decrease. Since not all citizens have the opportunity to allocate a large amount of money from their budget, annuity loans are more popular among the population.

There is a good reason why financial institutions also prefer annuity loans. With this form of lending, the borrower returns the funds in equal parts, but at first a significant part of the money goes to pay off interest on the loan, and not the loan body. The calculation of annuity payments on a loan is made in such a way that the client immediately deposits funds towards the payment of interest, and only a certain part of the payment, which increases over time, goes to repay the loan itself.

Since in the first period a significant part of the funds goes to repay the interest rate charged on the balance of the loan, the final cost of the loan will be higher than with a differentiated loan. The reason for this is the slower repayment of the loan body, from which interest is charged.

How to calculate the payment amount

As mentioned earlier, the annuity form of payments provides for a monthly transfer to the bank of the same amounts. In this case, the payment itself can be divided into two main parts:

1. The first part goes to pay off the interest on the loan. The size of this part gradually decreases closer to the end of the payment period.
2. The second part is used to return the "body" of the loan. With the annuity form of payments, this part gradually increases, reaching its peak towards the end of the loan repayment.

To figure out how to calculate annuity payments on a loan, you need to give a formula. Below we will consider a formula for calculating the amount of payments, as well as determining which part of the funds goes to pay interest, and which part goes directly to repaying the debt.

The formula for calculating is rather complicated. It takes into account many parameters, some of which are unfamiliar to the average consumer of financial institutions. It looks like this.

The indicators given in the formula mean:

1. MP– monthly loan payment;
2. Sz- the total amount of funds borrowed;
3. Mps- monthly interest rate;
4. Sk- the term of the loan (number of months) when interest will be accrued on it.

The formula for calculating an annuity loan payment, as already mentioned, is quite complicated. In order to calculate everything, you will have to use a calculator. To better understand how to calculate this parameter, a specific example should be given.

Example of calculating an annuity payment

In order to make a calculation, you need to know the total amount of the loan, interest on it, the monthly interest rate and the total period for which the loan was issued. In this case, the following parameters will be used:

1. The loan amount is 40 thousand rubles.
2. The rate is 22% per annum.
3. The term for which the money is taken is 2 years (i.e. 24 months).

Before using the formula, you need to set the value of one more parameter - the monthly interest rate. This is done as follows:

Mpc = annual interest rate / 100 / 12.

In this case, the monthly interest rate will be as follows:

22 / 100 / 12 = 0, 0183.

The calculation of a loan with annuity payments with such parameters is as follows:

40,000 x (0.0183 / (1 - (1 + 0.0183) -24)).

After all calculations, the following amount will be received - 2075 rubles 13 kopecks. This is how much money the client will have to pay monthly to close the loan.

Knowing the final amount of the payment, it is easy to calculate how much money will be overpaid after its final payment. To do this, you need to multiply the amount received earlier by the term of the loan:

2075 * 24 = 49,803 rubles. The final overpayment will be: 49,803 - 40,000 = 9,803 rubles.

How to make calculations easier

Since manual calculations are quite difficult, you can use the functionality of the Excel program included in the software package Microsoft office from Microsoft Corporation. Among the functions prescribed in it are "PLT", with which you can perform the necessary calculations.

The procedure is quite simple. You need to create a new table and write the following formula in any empty cell: "=PMT(22%/12; 24; -40,000) » . In this case:

1. "=PLT" - function.
2. 22%/12 - the annual interest rate.
3. 24 - term of the loan.
4. -40 000 - loan amount.

Sign «=» before the start of the formula is of great importance. Without it, the program will treat the input as plain text and will not perform calculations. All parameters must be entered exactly in the order in which they are indicated above. There must be a semicolon between them. Failure to follow these rules may result in an error during calculations. After entering the data, press the Enter key.

The program will calculate and give a result that will correspond to the amount obtained in the previous example. The use of Excel can significantly reduce the calculation time and make it easier for the borrower. However, there is an even simpler way to calculate the monthly payment.

Today, a large number of online calculators are posted on the Internet, with the help of which you can carry out the corresponding calculation. It is enough to enter the necessary data (loan amount, term and interest rate), and then complete the operation. The automatic system will independently calculate both the amount of the monthly payment and the total amount of payments along with the level of overpayment.

Deduction of funds that will be used to pay off the interest rate

The borrower can also independently calculate the amount of funds that are charged in accounting for interest payments. To do this, you need to use a special formula. It is much simpler than the previous one. How to calculate interest on a loan for annuity payments? It is necessary to multiply the amount of funds that still need to be deposited (that is, the current amount of debt on the loan) by the monthly interest rate.

As an example, it is worth calculating how much of 2075 rubles (the amount of the monthly payment received earlier) is spent on paying the interest rate on the first payment. In this case, the following formula applies:

• Cz (amount of debt on the loan) x Mps.

Since the payment will be the first, the debt at the time of its payment will be 40,000 rubles. Accordingly, from 2075 rubles to pay interest goes: 40,000 * 0.0183 \u003d 732 rubles. In the second payment: 38657 (debt at the time of the second payment) * 0.0183 = 707 rubles.

Having received this data, the borrower can easily calculate how much of the debt to the bank is actually repaid at the time of payment. To do this, it is enough to subtract from the payment amount the part that goes to interest. By carrying out this action, the borrower will receive the result - 1343 rubles (2075 - 732). At the second payment, the repayment of the body of the debt will take into account 1368 p. (2075 - 707).

Accordingly, during the first transfer of funds, despite the deposit of 2,075 rubles, the net debt (without interest rate) will decrease only by 1,343 rubles and amount to 38,657 rubles. In another month, the amount of debt will decrease to 37,289 rubles. Over time, more funds will be allocated for the repayment of the body, and less for the interest rate.

This approach to calculations allows the bank to calculate the interest rate from a larger amount than with differentiated payments. This, accordingly, increases the amount of funds that will eventually be transferred to interest accounting, and stretches the process of repaying the principal debt in terms of duration. That is, a citizen not only rallies more money as an interest rate, but also does this over a longer period of time.

Should I agree to an annuity loan repayment?

This form of repayment has its advantages. As mentioned earlier, the client will have to repay the loan by monthly transfers of small amounts. Since in most cases the bank is contacted individuals unable to allocate a large amount of funds from family budget, annuity payments can reduce the financial burden on a citizen.

Meanwhile, the example of calculating an annuity loan payment, given above, shows that in this case the borrower overpays significantly. With the parameters used in the example, the final cost of the loan will exceed the cost of the borrowed funds by approximately ten thousand rubles, which is disadvantageous for the borrower.

A differentiated loan is not accompanied by such a large overpayment. For this reason, it looks much more attractive. However, you must be prepared for large first payments on the loan (in some cases, many times the amount of transfers for annuity payments).

Thus, there are two main forms of calculating loan payments: differentiated and annuity. The second form involves the monthly payment of a fixed amount. It allows you to reduce the financial burden on the borrower, but is accompanied by significant overpayments on the loan. The formulas given above will give the borrower the opportunity to pre-calculate all the necessary data and decide on the advisability of taking an annuity loan.

So, friends, here we have reached the most interesting part - formulas and calculations related to annuity payments. Although lying, this topic is boring and uninteresting. Whoever is not “friends” with mathematics can now begin to yawn, and at a certain stage, fall into a stupor.

However, the site portal team decided to take a chance and write in simple words about formulas and calculations of annuity payments. What came out of it, you will find out by reading this publication.

Formula for calculating annuity payments

Are you sure you want to see the annuity payment formula? Okay, here she is:

P- monthly payment on an annuity loan (the same annuity payment that does not change during the entire loan repayment period);
S- amount of credit;
i– monthly interest rate (calculated according to the following formula: annual interest rate/100/12);
n- the period for which the loan is taken (the number of months is indicated).

At first glance, this formula may seem scary and incomprehensible. On the other hand, is it necessary to understand it? You just need to calculate the amount of the annuity payment, right? And what is needed for this? That's right, you just need to substitute your values ​​\u200b\u200bin the formula and make calculations. Let's get on with this now!

Calculation of annuity payment on a loan

Let's say you decide to take out a loan 50 000 rubles on 12 months under 22% per annum. Naturally, the type of repayment will be annuity. You need to calculate the amount of monthly installments on the loan.

First, let's beautifully arrange our initial data (we will need them not only in this, but also in further calculations):

Amount of credit: 50 000 rub.
Annual interest rate: 22% .
Loan terms: 12 months.

So, before you start calculating the annuity payment, you need to calculate the monthly interest rate (in the formula it is hidden under the symbol i and is calculated as follows: annual interest rate/100/12). In our case, the following will happen:

Now that we've found the meaning i, you can start calculating the size of the annuity payment on our loan:

By simple mathematical calculations, it turned out that the amount of monthly deductions on our loan will be equal to 4680 rubles.

In principle, this could be the end of our article, but you probably want to know more. Is it true? Tell me, do you want to know what proportion of these payments are interest on the loan, and what -? And in general, how much will you overpay on the loan? If yes, then we continue!

Loan repayment schedule with annuity payments

First, we will show you the annuity payment schedule itself, analyze it together with you, and only then tell you in detail about how and by what formulas we calculated it.

This is what our annuity loan repayment schedule looks like:

And this is a diagram (for clarity):

Both the graph and the chart confirm what was written in the publication:. If for some reason you have not read it, then be sure to do it - you will not regret it. And those who have read can be convinced that in the annuity loan repayment schedule, payments are made in equal amounts, for initial stage the share of interest on the loan is the highest, and closer to the end of the term it decreases significantly.

Please note that the body of the loan is repaid from the first month of lending. It’s just that on some sites you can read something like this: “With an annuity loan repayment scheme, interest is paid first, and only then the body of the loan itself.” As you can see, this statement is not true. It would be more correct to say this:

Annuity payments contain a high proportion of interest on the loan at the initial stage.

The body of the loan is also repaid from the first month of lending. This reduces the amount of debt and, accordingly, the amount of interest payments on the loan.

Now let's take a closer look at our annuity payment schedule. As you can see, our monthly payment is 4680 rubles. It is this amount that we will pay to the bank every month throughout the entire loan period (in our case, throughout 12 months). As a result, the total amount of payments will be 56 157 rubles. We took out a loan 50 000 rubles(in the graph, this is the fourth column, which is called “Repayment of the loan body”). It turns out that the overpayment on this loan will be 6157 rubles. Actually, this is the interest on the loan, which is indicated in the third column of our annuity payment schedule. It turns out that (or) we will have - 12,31% . Let's make it "beautiful" this information:

Monthly annuity payment: 4680 rub.
Loan body: 50 000 rub.
Total payout: RUB 56,157
Overpayment (interest) on the loan: 6157 rub.
Effective interest rate: 12,31% .

So, we have analyzed the schedule of annuity payments. It remains to understand how the percentage and share of the loan body in monthly payments. That is why in the first month the interest is exactly 917 rubles, in the second - 848 rubles, in the third - 777 rubles etc.? Do you want to know? Then read on!

Calculation of interest on annuity payments

I n- the amount in the annuity payment, which is used to pay interest on the loan;
S n- the amount of the remaining debt on the loan (loan balance);
i- the monthly interest rate already familiar to you (in our case, it is equal to - 0.018333 ).

For clarity, let's calculate the percentage of interest in the first payment on our loan:

Since this is the first payment, the amount of the remaining debt on the loan is the entire loan - 50 000 rub. Multiplying this amount by the monthly interest rate - 0.018333 , we will get 917 rub.– the amount indicated in our schedule.

When calculating the amount of interest in the next annuity payment, the monthly interest rate is multiplied by the debt that was formed at the end of the previous month (in our case, this is RUB 46,237). The result will be 848 rub.- the size of the share of interest in the second annuity payment. Interest is calculated on the same principle in other payments. Next, let's calculate the component in annuity payments that will be used to repay the loan body.

Calculation of the share of the loan body in annuity payments

Knowing the share of interest in the annuity payment, you can easily calculate the share of the loan body. The calculation formula is simple and clear:

S- the amount in the annuity payment, which goes to repay the body of the loan;
P- monthly annuity payment;
I n- the amount in the annuity payment that goes to pay off the interest on the loan.

As you can see, there is nothing complicated here. In fact, an annuity payment contains two components:

1. 1. Share of interest on the loan.
2. 2. Share of the body of the loan.

If we know the value of the annuity payment itself and the size of the percentage, then what remains after deducting the amount of interest from it will go to repay the body of the loan in this payment.

The calculation of the share of the loan body in our first payment looks like this:

We hope that now everyone understands where the amount came from in the “Repayment of the loan body” column of our annuity payment schedule in payments for the first month 3763 rub. Yes, yes, this is exactly what is left after we from the amount of the annuity payment ( 4680 rub.) subtracted the amount of interest on the loan ( 917 rub.). The values ​​of this column for the following months are calculated in a similar way.

So, we figured out the body of the loan. Now it remains to find out how the debt is calculated at the end of the month (in the annuity payment schedule, this is our last column).

How to calculate the debt at the end of the month in the annuity payment schedule

First of all, you need to understand what exactly is your loan debt, and what payments contribute to its reduction. In our example, you borrow 50 000 rubles- that is your duty. Overpaid loan interest ( 6157 rubles) are not your debt, this is just a reward to the bank for the loan. Thus, we can conclude:

Paying interest on a loan does nothing to reduce your debt to the bank.

In times of crisis, banks often "go ahead" with their debtors. They say something like this: “We understand that you are in trouble now! Okay, our bank is ready to make concessions to you - you can just repay the interest to us, but you don’t need to repay the body of the loan. All people are brothers and should help each other! Blah blah blah…"

At first glance, such an offer may seem profitable, and the bank itself - "a white and fluffy lapule." Yep, no matter how! If you pick up a calculator and carry out simple arithmetic calculations, it immediately becomes clear that the real offer of the bank looks something like this:

“Guys, you got money! There's nothing you can do, that's life! We offer you to temporarily (and maybe forever) become our slave - you will pay interest on the loan every month, and you don’t need to repay the debt itself (well, so that the amount of interest payments does not decrease). Nothing personal - it's just business, friends!

Now remember the main idea:

It is the repayment of the body of the loan that pulls you out of the debt hole. Not interest, namely the body of the loan.

Surely you have already guessed how the debt at the end of the month is calculated in our payment schedule. In general, the formula looks like this:

S n2- debt at the end of the month on an annuity loan;
S n1- the amount of current debt on the loan;
S- the amount in the annuity payment that goes to repay the body of the loan.

Note! When calculating the debt at the end of the month, only that part of the payment that goes to repay the loan body is deducted from the total amount of the current debt (paid interest is not included here).

For clarity, let's calculate what the debt at the end of the month on our loan will be after making the first payment:

So, on the first payment current debt on a loan we have equal to the entire amount of the loan ( 50 000 rub.). To calculate the debt at the end of the month, we subtract from this amount not the entire monthly payment ( 4680 rub.), but only the part that went to repay the body of the loan ( 3763 rub.). As a result, our debt at the end of the month will be RUB 46,237, it is on this amount that interest will be charged in the next month. Naturally, they will be less, as the amount of debt has decreased. Now you understand why it is important to repay the body of the loan?

What is more beneficial directly to the recipient borrowed money annuity or differentiated payment type? Small comparative analysis shows the main differences between the two schemes:

• annuity loan repayment scheme comes out as a result expensive differential circuit, and this is especially noticeable at large interest rates and long loan terms;
• initial payments with a differentiated scheme, compared with an annuity, more are obtained;
• in the lending market, they primarily offer an annuity loan repayment scheme, due to significantly reduced requirements for minimum size confirmed income of the borrower;
• at early repayment in the case of using the annuity payment scheme, the cost of the loan decreases, since a significant amount of interest is repaid during the first payments on the loan;
• when providing a loan with a differentiated repayment scheme financial institutions check more carefully solvency potential borrower, since at the first stages of repayment of the loan, he needs to repay a significant part of the funds received.

However, the final choice of the repayment schedule and scheme remains with the potential borrower.

Credit calculator

Credit calculator is a toolkit for calculating the main parameters of a loan, implemented through a web interface, usually a website banking institution. The online loan calculator is a quick way to plan repayments as principal loan funds and interest accrued on the balance of the used credit limit.

Using our loan calculator, you can make payments using differentiated or annuity payments.

Annuity payment– monthly repayment of received credit funds by making uniform fixed payments. Annuity repayment is represented by two parts - a fee for the use of credit funds and the amount that is directed to repay the loan itself.

Differentiated payment is carried out on a monthly basis, the amount of payment is reduced in direct proportion to the period until the end loan agreement. The differentiated payment structure is also formed from two parts - once fixed amount debt repayment and a decreasing part of the loan cost, the calculation of which is based on the balance of the loan body.

Today, most credit institutions use the scheme of annuity payments in their practice.

Among other things, credit calculator acts as an excellent comparative tool for various types of loans, which allows you to contact banking specialists only directly for the issuance of borrowed funds. Calculate a more profitable and convenient loan payment scheme on our loan calculator.