Every man at least once in life faced with the need to take out a loan. The Bank provides the borrowed funds at a certain percentage, for a specified period. If a client is satisfied with the terms of service and the financial institution is the creditworthiness of the borrower, signed the contract. It must specify the item on the schedule of debt repayment: in equal installments or reducing the balance owed. In this article you will know that this annuity and differential payment types.


Annuity payments are of equal amounts over equal intervals. They include the principal debt and remuneration of financial institutions. Annuity and differentiated payments differ in the structure of the repayment of the loan. In the first scheme for the payment of interest is initially directed most of the funds. In the second case, the body of the loan divided by the number of payments equal parts. And interest accrued on the principal balance. Therefore, in the differential circuit of the first payment large enough. It should be noted that in practice, loans without collateral are repaid in equal installments, but in the long term loans are available to both schemes. Select the option only at the time of application. After signing the documents to change it will not happen.

Annuity and differentiated payments: formula, calculator, differences

How to calculate

Annuity and differentiated payments

Annuity and differentiated payments formula

Any loan is composed of loan and interest for its use. Differential payments to pay the principal sent every month to the same amount of money. The decreasing part is the interest on the loan. They are calculated from the sum of the outstanding balance. With the repayment of the loan reduced interest, and with them the monthly payment. It is calculated in several stages.

1. To determine the amount of the repayment of the loan:

  • OS – principal debt
  • SK - the initial loan amount;
  • KP – the number of payments.

2. Further calculations depend on the Bank of a temporary base. Some financial institutions proceed from the rule that a year consists of 12 months, and accordingly calculate the amount of interest:

  • OK — the loan balance in the calculation period
  • — Interest rate (per annum).

Other banks use a more thorough approach. As a design base, they did not take the number of months and days in a year (365):

% = OK * * (CHDM 365), where:

  • OK — the loan balance in the calculation period
  • С - interest rate (annual);
  • CHDM — number of days in the month (28-31).

To calculate the balance owed for the period you need the size of the principal payment multiplied by the number of paid periods. Then, the resulting sum subtracted from the total:

OK = SK \u0026 ndash; (OS * KP), where:

  • SK - the initial loan amount;
  • OS – principal debt
  • KP \u0026 ndash; number of periods.

Equal payouts

Annuity payments do not change until the end of the term of the contract. The only exception is the early repayment of the loan. The annuity payment consists of two parts: the body of the loan and interest for its use. Their structure over time changes. And the size is calculated by the following formula:

AP = SC * [C (1- (1 + C) -kp], where:

  • С - annual interest rate;
  • SK - the initial loan amount;
  • KP — the number of periods.

This is a classic formula used by most banks.

Other ways

In some cases we use the scheme of annuity payments where the first payment is not equal to all previous.

AP = SC * [(S (1) CP-1 – 1)], where:

  • С - annual interest rate;
  • SK - the initial loan amount;
  • KP — the number of periods.

This initial payment is less than ordinary, but always includes interest. But if the Bank uses as a base “365 calendar days”, a great interest rate and long loan term, this amount can be much larger than all subsequent ones.

Sometimes a scheme is used in which you can meet annuity and differential payments: the first and the last are different from all the others.

AP = SC * [C + (C (1 + C) kp-2 - 1)], where:

  • С - annual interest rate;
  • SK - the initial loan amount;
  • KP — the number of periods.

In this scheme, the first and the last payment includes interest on the loan. A large part repaid from the very beginning and the rest at the end of the period. Overpayment on the loan is already included in the annuity and differential payment. The difference is obvious: in the first case, the Bank receives fees from a large volume, and the second

The smaller annuity payment represented in the classical scheme, the largest in the last. The less time left until the end of the term of the contract, the greater this difference. It is important to consider in the early repayment of the loan.

Secret disclosure

The Bank provides money to borrowers at interest. And when are they scheduled debt repayment in the first payments, most of the money goes to pay interest. Long-term loans, this ratio may be even 90:10. This scheme is used in any schedule of repayment. For several reasons for this. The main is that this way, the Bank insures against the insolvency of customers. For example, if a mortgage contract a year after signing the documents received a letter asking for the extension of credit, even if the new schedule will be drawn up with a delay of 3-6 months, your profit Bank by this time have already received. The new interest will continue to accrue again on the body of the loan.

Annuity or differential payment: who pays less

We considered several schemes for debt repayment. To date, there are annuity and differentiated payments as well as mixed cases in which the interest repaid separately from the principal amount. What is the best option to choose? The borrower more available annuity – equal payments throughout the term of the contract. The amount of principal decreases slowly, while the total amount of accrued interest is much greater. If the client decides to prepay the loan in full, then, in fact, he will repay the loan in full. In the scheme of various scaled payment of such financial loss will not. Even if early repayment of the mortgage agreement will be the beginning of its validity.

Therefore, banks are increasingly using annuity scheme. In addition to the previously mentioned reasons quick income is another psychological aspect – the client is easier to remember one amount every month and send it to debt repayment. And personal budget planning easier. In addition, banks, in deciding to issue the loan to the client and in what amount, and calculate the ratio of the payment to count income. And because in the differential scheme the first payment is always greater in volume than the last, and a chance to get a loan turns out smaller.

Despite all above-mentioned arguments, a clear answer to the question of which type of payment (annuity, differentiated) to choose. If the contract is for a short period, and the monthly income of the client allows you to make large sums at the beginning of its validity period, it is best to choose various scaled scheme. Another thing that banks do for short-term credits practically do not give. And in the case of long-term loans this scheme can swipe the wallet of the client.