# Annuity payments - what is it? Description and formula for calculating annuity

Depending on the chosen credit program, the client may be offered several debt repayment schemes. The most common of them - differentiated and what it is and how they are calculated, you will learn from this article.

## Definition

An annuity is an equivalent monthly payment that is set once for the entire duration of the contract. It is convenient to use it at the long period of crediting. There is no need to constantly remember what amount you need to pay to the bank. On the other hand, with a large debt drawn up for a long period, the client first repays interest and then the loan body. At the same rate, the amount and terms of overpayment in the annuity scheme will be more than in differentiated. This is beneficial to banks, as they will get more profit in the form of interest.

In a differentiated scheme, the payment amount will decrease by the end of the contract term. Payments on the body of the loan are equal, and interest is calculated on the loan balance.This scheme uses a small number of banks and only in long-term lending programs. It is less beneficial for credit institutions, since the amount of overpayment is less. This is also an advantage for customers. At the same time, with long-term loans, the first payments will be very large. Such costs are heavily beaten.

## Formula

The calculation of annuity payments is as follows:

A = K x S, where

- A - annuity payment,
- K - coefficient
- S is the loan amount.

The coefficient is calculated as follows:

K = i x (1 + i)n\ (1 + i)n- 1, where:

Schedule differentiated payments is calculated by the formula:

P = OZ / PP + OZ x S, where:

- P - monthly payment;
- OZ - debt balance;
- PP - the number of periods to complete repayment of the loan;
- C - monthly interest rate.

The method of calculating the differential payment:

- The amount payable is divided by the number of months.
- To the resulting figure is added the percentage for the month of use of money.

## Example

The client issued a loan of 30 thousand rubles. at 18% per annum for 3 years. Initial data:

- S = 30 thousand rubles.
- The conditions specified annual rate. According to this formula, it cannot be used to calculate annuity payments.What does it mean? The annual rate should be divided by 12 and get the amount of interest that the client will pay monthly: i = 18% / 12 = 1.5%.
- As a result, we obtain: n = 3 x 12 = 36 months.

Substitute all the values in the formula:

K = 0.015 x (1 + 0.015)36\ (1 + 0,015)36- 1 = 0,03615

The amount of the annuity payment will be: A = 0.03615 x 30 = 1.08457 thousand rubles.

## Alternative option

The program in which you can independently conduct the calculation of annuity payments - Excel. For this, a special function is provided (= PMT). It can be called by pressing the “fx"On the left side of the search box. In the new window you need to fill in the following parameters:

- "% \ 12" - the annual commission of the bank in percent;
- "Kper" - the number of periods, months;
- "PS" - the initial loan amount (in the formula, it is always put with a minus).

The same parameters can be entered into the cell without calling the window with the formula: = PMT (Rate \ 12; To lane; -Pc).

Specifically for the conditions of the previous example, this formula will look like this: = PMT (18% / 12; 36; -30000).

You can also use the annuity payment calculator, which is presented on the website of most banks. It allows you to calculate the cost of services taking into account the selected lending program. The user only needs to enter the initial data in a special form.

## Which scheme is better to choose

When a mortgage or car loans to the client is not profitable annuity payments. What does it mean? The client will overpay more on interest. In a differentiated scheme, the loan body is repaid in equal parts. At the same time decreases the amount of interest. But there is a reverse side of the coin. The amount of the first payments may differ significantly from the last. Far from every client can afford such expenses. And the bank will take this into account, counting the credit limit. Depending on the internal rules of the organization, the monthly payment should not exceed 20-25% of income. If a customer wants to be serviced on a differentiated basis, he must have a high salary. Especially if a loan is issued on a car or mortgage. Annuity payments help plan the budget. The borrower pays the same amount every month. Another thing is that in the early stages almost all the money goes to pay interest. The balance changes from the middle of the term. On the other hand, such a scheme would be beneficial for entrepreneurs who take a loan for the maximum amount for business development and plan to increase income in the near future.

## Early repayment conditions

Every borrower asks this question. Indeed, in the contracts may be prescribed a commission for early repayment of the debt. But the bank does not have the right to charge “future” interest. It is written in the Civil Code. The bank may also impose certain limits, for example, to prohibit early repayment of the loan for the first 2-3 months. The profit institution in any case will receive. After all, the scheme of calculating monthly annuity payments implies the immediate repayment of interest, and then the principal debt. Sometimes other options are offered:

- recalculate the debt schedule in the direction of increasing the payment;
- limit one payout to 2, 3x monthly installments, etc.

## Interest return

As mentioned earlier, the annuity payment is an interesting way for the bank to repay the debt, since money goes first to pay off the interest, and then to the loan body. The borrower will be comfortable with the fact that during the entire term of the contract the amount of expenses will be fixed. The nuance is that in case of early repayment of the debt, the bank will receive more profit in the form of interest. But the borrower can return part of the amount paid, even in the case of refinancing.By law, the bank can make a profit only for the period of actual use of money by the client. Therefore, he has the right to demand a part of interest back (Article 809 of the Civil Code of the Russian Federation).

The client is able to independently calculate how much money he can return. To do this, you need to subtract from the sum of all accrued interest that part, which falls on the months before the real repayment. These data can be found in the payment schedule attached to the contract. With a long term loan the figure can be impressive.

*Example*

On the mortgage in the amount of 2 million rubles, executed for 20 years at a rate of 13.75%, the client must pay interest totaling 3.9 million rubles. If the loan was repaid in three years, then 230 thousand rubles, that is, a quarter of the amount paid, will be returned. This data can also be obtained by using the annuity payment calculator.

But not all customers are aware of this right. And with a consumer loan, the amount of overpaid interest can be several hundred rubles. Not everyone wants to sort out relations with the bank on this issue and spoil their reputation in the future.

## Benefits

- Annuity payment is more often used in consumer loans.
- It is convenient for the borrower - a fixed amount of costs.
- Its easy to calculate.
- Such a scheme would be particularly suitable for people with a fixed and low income.
- Customers can count on a larger loan limit.

## disadvantages

- Interest is paid off first, and then the loan body.
- Early repayment is possible, but with certain conditions: either the amount of the payment is limited, or the period during which the client must use the service (for example, the first 2-3 years) is indicated.

When choosing a mortgage program, the weight of the first differentiated payments is mitigated by the ability to refinance the debt. In the annuity scheme, the financial burden imposed on the borrower remains unchanged under any circumstances. Given this, banks in long-term lending programs offer customers two schemes to choose from. Consumer loans to financial institutions do not care about customer problems, they simply throw off debts to collectors.

Today, one person can apply for 5-6 loans with an annuity repayment scheme. This form of payment has received great social value. But it is dangerous both for clients who have issued an inordinate amount of loans, and for banks, which have not studied in detail the financial condition of the borrower.

## Conclusion

The method of repayment of the loan is of great importance for the borrower.Especially if he already has several loans. Today, differentiated and annuity payments are used. What does it mean? In the first case, the payment amount is reduced in proportion to the duration of the loan. In the second scheme, loan costs are fixed and do not change throughout the entire period of the contract. The client can independently carry out the calculation of annuity payments. Excel has a built-in function for this purpose (= PMT).