Today, many are familiar with annuity payments due to the widespread use of this method of repaying loan obligations. However, annuity is not only a banking term. It occurs in various fields - from insurance to retirement, in which it is used to indicate regular payments / payments. Initially, this word implied annual periodicity (from the Latin "annuus" - "annually"). However, in the modern interpretation, clear boundaries are washed away, and annuity is any regular identical payments (daily, monthly, quarterly, etc.). Two main characteristics of this type of payment are the frequency and invariability of the amount paid.
However, not all components of an annuity are constant values. Take for example an agreement made with a banking organization. So, when applying for a loan, the borrower agrees to pay the lender regularly (usually monthly) a certain amount of funds (annuity payments) to repay the loan. Moreover, this value includes both part of the principal loan amount and interest on its use. It is they who change in time. Initially (before the middle of the loan term), the amount of interest paid exceeds the principal repayment amount, then (after the middle of the loan term) the situation changes dramatically, and the borrower’s debt already accounts for most of the annuity.
How is annuity calculated in this case? For a more understandable explanation, we give an example. Suppose a loan agreement has been concluded with the following conditions: loan term - one year (from November 28, 2013 to November 28, 2014); interest rate - 20% per annum; loan amount (principal) - 150 thousand rubles. We are interested in the amount of monthly payments (annuity) and loan overpayment (borrowed price). The payment, which must be paid on December 28 (and each subsequent month), is calculated on the basis of the formula:
PA post = R * (1 - (1 + i) - n ) / i, where
PA post - the amount of the loan (or the present value of the annuity, is 150 tons);
R - monthly payment amount;
i - monthly interest rate (20% / 12 = 1.67);
n is the number of lending periods (12 months).
Thus, R (or annuity) is a value equal to:
PA post * i / (1 - (1 + i) - n ) = 150000 * 0.0167 / (1 - (1 + 0.0167) -12 ) = 13898 rubles.
Now it’s easy to determine how much the loan overpayment will be with our conditions:
13898 * 12 - 150000 = 16776.
Such a price will have to pay for using the money of the bank. Using the formula in Excel, you can build a plate on which the components of the annuity payment (interest and part of the principal debt that you will pay each month) will be painted, recall that they change. It is not difficult to calculate them, just monthly you need to reduce the main debt by the amount already paid and multiply it by the interest rate (as you know, it is charged exactly on the balance of the debt).
Of course, the annuity method brings significant benefits to the bank, because initially the borrower pays mainly interest, and only then does the repayment of the principal amount begin. And the longer the client pays the loan, the more the credit institution will earn. That is why banks are not very fond of when a loan is repaid early (until recently, in this case, a commission was often charged, which was canceled by law).
This feature of annuity payments (change of components) is typical for loans. Usually, an annuity is simply a fixed amount, the payments of which are made with a given frequency. An example of this is in other areas: rent, rent, pension, depreciation contributions, regular payments by an insurance company to policyholders or, conversely, insurance premiums, an annual fee, etc.