What is more profitable directly for the recipient of borrowed funds annuity or differentiated payment type? A small comparative analysis shows the main differences between the two schemes:

• annual loan repayment scheme comes out in the end more expensive Differentiated scheme and this is especially noticeable at large interest rates and long loan periods;
• initial plates with a differentiated scheme, compared with the annuity, more obtained;
• in the lending market, primarily offer the annuity scheme of loan repayments, due to significantly reduced requirements for the minimum size of a borrower's confirmed income;
• for early repayment In case of using an annuity payment scheme, the loan cost decreases, since a significant amount of interest is repaid during the first loan payments;
• when granting a loan with a differentiated repayment scheme Financial institutions more carefully check solvency The potential borrower, since in the first stages of the loan return, it needs to pay a significant part of the funds received.

However, the final choice of graphics and the repayment scheme remains behind the potential borrower.

Credit calculator

Credit calculator It is a toolkit for the calculation of the basic credit parameters implemented through the web interface, as a rule, the site of the banking institution. Credit Calculator Online This is a quick possibility of planning repayments as the principal amount of credit funds and interest accrued to the balance of the credit limit used.

With the help of our credit calculator, calculations can be calculated using differentiated or annuity payments.

Annuity payment - Monthly repayment of credit funds by making uniformly fixed payments. An altitude repayment is represented by two parts - a fee for the use of credit and the amount that is sent to repay the loan itself.

Differentiated payment It is carried out on a monthly basis, the amount of payment decreases directly proportionally until the end of the loan agreement. The structure of the differentiated payment is also formed from two parts - once the established amount of the return of debt and the decreasing part of the loan value, the calculation of which comes from the balance of the loan body.

Today, the majority of credit institutions are used in their practice it is the scheme of Annicate payments.

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

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

Annuity payment is calculated based on the annuity coefficient of the following form:

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

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

The amount of payment during an annuity method of repayment depends on the calculated annuity (K) coefficient and the value of the body of the loan and is defined as follows:

TC - the body of the loan (issued amount).
AP is an annuity payment.

Next, we give our mathematical formulas to practical. Since the interest rate is annual, and the repayment of the loan is carried out monthly, i.e. 12 times a year, the formula for calculating an altitude payment takes the following form:

k - the number of months during which loan repayment is assumed.

As we have already said earlier, the amount of annuity payment is distributed to the repayment of the body of the loan and accrued interest. As interest is charged monthly to the amount of the loan debt balance, the formula for calculating them has the following form:

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

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

Typically, banks are used as a temporary base of 12 months, but some financial institutions produce calculations, based on the number of no months, and days a year (usually 365 days): Then the result is more accurate.

With the practical application of this methodology can be found in the following examples:

• an example of calculating annuity payments by the Sberbank educational loan obtained to pay for the Skolkovo MBA training program. Comparison with a differentiated repayment method;
• an example of calculating interest and consumer loan consumer credit schedule provided without ensuring. An example is considered annuity and differentiated ways of repayment.

Annuity payment - A variant of the monthly payment on the loan, when the size of the monthly payment remains constant for the entire lending period.

Monthly payment, with an annuity loan repayment scheme consists of two parts. The first part of the payment goes to repay interest for the use of the loan. The second part goes on debt repayment. An annuity repayment scheme differs from differentiated in that at the beginning of the credit period, percentages constitute most of the payment. Thus, the amount of the principal debt decreases slowly, respectively, the overpayment of interest with such a loan repayment scheme is obtained.

With the annuity scheme of loan payments, the monthly payment is calculated as the amount of interest accrued for the current period and the amount going on to repay the loan amount.

To calculate the size of the monthly payment, you can use. With the help of a credit calculator, you can determine the size of the accrued interest, as well as the amount that goes on debt repayment. In addition, you can take a regular calculator and calculate the payment schedule manually.

Calculation of annuity payment

Formula, to determine which part of the payment went to repay a loan, and what percentage is quite complicated and without special mathematical knowledge, a simple inhabitant will be difficult to use it. Therefore, we will calculate these values \u200b\u200bin a simple way that gives the same result.

To calculate the percentage component of the annuity payment, you need a loan balance for the specified period to multiply by an annual interest rate and divide all this to 12 (the number of months per year).

To determine a part going on debt repayment, it is necessary to subtract accrued interest from the monthly payment.

Since a part that matures on the repayment of the principal debt depends on previous payments, therefore the calculation of the schedule, according to this method, calculate consistently, starting from the first payment.

An example of calculating the schedule of payments on the annuity loan

For example, we calculate the schedule of payments on a loan in the amount of 100,000 p. and an annual interest rate of 10%. We take 6 months of loan repayment.

To begin with, we calculate the monthly payment.

Then we will calculate the percentage and credit part of the annuity payment.

If it is interesting to know the amount of overpayment over the annuity loan, the monthly payment is necessary, multiply by the number of periods and from the received subtraction of the initial loan size. In our case, the overpayment will be as follows:

17156,14 * 6 – 100000 = 2936,84

The result of calculations in our example on the site will look like this:

What confirms the correctness of our calculations.

So, friends, so we got to the most interesting - to formulas and settlements related to annuity payments. Although we are, this topic is boring and uninteresting. Who is not "friendly" with mathematics can now start to yawn, but at a certain stage - to go into a stupor.

Nevertheless, the portal site team decided to risk and write simple words about formulas and calculations of annuity payments. What happened from this, you will learn by reading this publication.

The formula for calculating annuity payments

Are you sure that you want to see the formula of an annuity payment? Well, here she:

P. - Monthly payment on the annuity loan (the one annuity payment that does not change during the entire repayment period);
S. - credit amount;
i. - Monthly interest rate (calculated according to the following formula: Annual interest rate / 100/12);
n. - The term for which a loan is taken (indicates the number of months).

At first glance, this formula may seem terrible and incomprehensible. On the other hand, whether it is necessary to understand it? You also need to calculate the amount of annuity pay, 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 now do it now!

Calculation of an annuity loan payment

Suppose you decided to get on credit 50 000 rubles on the 12 months under 22% annual. Naturally, the repayment type will be annuity. You need to calculate the amount of monthly loan contributions.

Let us first embrace our source data (they will need not only in this, but also in further calculations):

Credit amount: 50 000 rubles.
Annual interest rate: 22% .
Loan terms: 12 months.

So, before proceeding to the calculation of the annuity payment, it is necessary to calculate the monthly interest rate (in the formula it is hidden under the symbol i. And it is calculated: an annual interest rate / 100/12). In our case, the following will be:

Now that we found a value i., It is possible to start calculating the amount of annuity pay on our loan:

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

In principle, this could be finished to finish our article, but you probably want to know more. Truth? Tell me, you want to know what share in these payments is interest on the loan, and what -? And in general, how much do you overpay the loan? If yes, then we continue!

Credit repayment schedule annuity payments

First, we will show you the schedule for annuity payments yourself, will analyze it together with you, and then we will then tell you in detail about how and for what formulas we calculated it.

This is how the annuity schedule of repaying our loan looks:

And this is a diagram (for clarity):

Both graph and chart confirm written in publication :. If for some reason you have not read it, then you must do it - you will not regret it. And those who read, can make sure that in the annuity schedule for repayment of the loan payment is carried out equal amounts, at the initial stage, the share of interest on the loan is the highest, and closer to the deadline it is significantly reduced.

Pay attention to the fact that the loan body is repaid from the first month of lending. Just on some sites you can read something like this: "With an annuity loan repayment scheme, percentages are paid first, and then the loan body itself." As you can see, this statement does not correspond to reality. It will be more correct to say:

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. Thus, the amount of debt decreases and, accordingly, the amount of interest payments on the loan.

Now let's study our annuity pay schedule more detailed. As you can see, the monthly payment we have 4680 rubles. It is this amount that we will pay the bank every month throughout the term of credit (in our case - throughout 12 months). As a result, the total amount of payments will be 56 157 rubles. On credit we took 50 000 rubles (In the graph, this is the fourth column, which is called "repayment of the body of the loan"). It turns out that overpayment on this loan will be 6157 rubles. Actually, this is the interest on the loan, which are indicated in the third column of our annuity payments. It turns out that (or) we will be - 12,31% . Let's "beautifully" to issue this information:

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

So, we analyzed the schedule of annuity payments. It remains to understand how the percentage of the loan body in monthly payments is calculated. That is why in the first month 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 goes to repay interest on the loan;
S N. - the amount of the remaining debt on the loan (balance of the loan);
i. - Already familiar to you a monthly interest rate (in our case, it is equal - 0.018333 ).

Let's calculate the interest in the first payment on our loan for clarity.

Since this is the first payment, the amount of the remaining debt on the loan is all credit - 50 000 rubles. Multiplying this amount for a monthly interest rate - 0.018333 , we get 917 rubles. - the amount specified in our chart.

When calculating the amount of interest in the next annuity payment, a debt is multiplied by a monthly interest rate that formed at the end of the previous month (in our case it 46 237 rub.). As a result, it turns out 848 rubles. - The size of the interest of interest in the second annuity payment. In terms of the same principle, interest in other payments are calculated. Next, let's calculate the component in annuity payments, which will go to the repayment of the loan body.

Calculation of the share of the body of the loan 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 understandable:

S. - the amount in the annuity payment, which goes to the repayment of the body of the loan;
P. - Monthly annuity payment;
I N. - The amount in the annuity payment, which goes to repay interest on the loan.

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

1. 1. The 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 interest rate, then the repayment of the body of the loan in this payment will go what will remain after subtracting the amount of interest from it.

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

Now we hope to all understand everything from where in the column "Repayment of the body of the loan" of our schedule of annuity payments in payments for the first month, the amount took 3763 rub. Yes, yes, it is exactly what remained after we are from the amount of annuity pay ( 4680 rub.) I detected the amount of interest on the loan ( 917 rubles.). Similarly, the values \u200b\u200bof this graph over the subsequent months are calculated.

So, with the body of the loan sorted out. Now it remains to find out how debt is calculated at the end of the month (in the chart of annuity payments it is our last column).

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

First of all, it is necessary to understand what exactly is your debt on the loan, and what payments contribute to reduction. In our example, you take on credit 50 000 rubles - This is your duty. Overpaid on loan interest ( 6157 rubles) Your debt is not, it is just a bank reward for the loan provided. Thus, we can conclude:

Repayment of interest on the loan does not contribute to the reduction of your debt to the bank.

In crisis times, banks often "go towards their debtors. They say something like this: "We understand, you have problems now! Okay, our bank is ready to go for concessions - you can simply repay interest, and the body of the loan itself is not necessary. Yet people brothers and must help each other! Blah blah blah…"

At first glance, such a proposal may seem favorable, and the Bank itself is "White and Fluffy Lapuli". Yeah, no matter how! If you take into the hands of a calculator and conduct simple arithmetic calculations, it immediately becomes clear that the real offer of the bank looks approximately as follows:

"Guys, you got for money! Nothing can do it, this is life! We offer you for a while (and maybe forever) become our slave - you will pay monthly interest on the loan monthly, and the debt itself is not necessary (well, that the amount of interest payments does not decrease). Nothing personal - it's just business, friends! "

Now remember the main idea:

It is repayment of the body of a loan pulls you out of the debt. Not percent, but the body of the loan.

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

S N2. - debt at the end of the month over the annuity loan;
S N1. - the amount of current loan debt;
S. - The amount in the annuity payment, which goes on the repayment of the body of the loan.

Note! When calculating the debt at the end of the month, only the part of the payment is taken away from the total amount of current debt, which goes to the repayment of the body of the loan (the percentages paid here are not included).

Let's consider it for clarity, what will be the debt to the end of the month on our loan after making the first payment:

So, at the first payment, the current loan debt is equal to the entire amount of the loan ( 50 000 rubles.). To calculate the debt at the end of the month, we take away 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 46 237 rub., It is for this amount that interest will be accrued next month. Naturally, they will be less, since the amount of debt decreased. Now you understand why it is important to repay the body of the loan?

Annuity payment is distinguished by the specificity of calculation and payments - equal parts over the entire period of credit consisting of a loan percentage and the amount of the principal debt. Modern banks practice predominantly annuity payments in lending, due to high profits percentage.

• A - the amount of payment;
• K - annuity coefficient;
• S is the initial credit amount.

If you do not know the coefficient, it can also be calculated by the formula:

K \u003d i * (1 + i) n / ((1 + i) n -1)

• i - Monthly rate;
• n - the number of months for which the loan should be repaid.

If the monthly rate is unknown, divide the annual interest rate by 12.

What is an annuity payment on the loan?

How to figure out what an annuity payment on the loan? This is a regular contribution amount to repay a loan. A characteristic feature of such a payment is equal amounts of repayment: all the designated credit period you will make the same amount into which the loan body includes a loan percentage.

Since 2012, borrowers may early to pay a loan without prejudice to the wallet. Due to the fact that many lender lifestators are looking for a way to return the debt ahead of schedule. However, it is important to calculate in advance how winning it is.

During annuity payments, interest is essentially advanced. For example, you have a loan for 6 months, however, you used it only for 4 months, we put out on the fifth. It turns out that at the first payments you have made the amount of interest, as if used in the 5th, 6th months.

With ordinary repayment, interest is paid according to the schedule. If the start-up payment will be occurring, overpaid by annuity.

What is a schedule of annuity payments?

An altitude payment schedule is calculated so that each monthly payment is the same. Interest Bank charges on the balance of debt, so their amount is reduced monthly, respectively, the amount of body repayment will increase.

Therefore, in the first payment, interest payments will be the bulk, and in the latter - the body of the loan.

How to use an altitude calculator?

Many banks, private credit firms post an online annuity payments calculator on official sites.

It is enough to introduce a monthly percentage to the corresponding fields to enter the corresponding fields, the number of months (lending period), the full amount of the loan. The program will automatically calculate your monthly payment, the sum of all payments and interest.

Repayment of annuity payments

Repayment of annuity payments is the process when payments will be less payments for other payment systems. This is due to the fact that the borrower initially extends almost some credit interest, and the main duty remains almost intact. Therefore, the annuity of the repayment makes it possible to get a loan to people with a small solvency.

Tip from Compare.ru: The low amount of payments is not too reflected on the family budget, and the high cost of credit funds is gradually felt less due to the inflationary state processes. Annuity payment is beneficial when making a mortgage loan, because it allows you to plan a budget for several years in terms of.