Annuity is the payments we face everywhere

2024 Author: Howard Calhoun | [email protected]. Last modified: 2024-01-02 13:48

Today, many are familiar with annuity payments due to the widespread use of this method of repaying credit obligations. However, annuity is not only a banking term. It is found in various fields - from insurance to pensions, in which it is used to denote regular payments / payments. Initially, this word meant annual periodicity (from the Latin "annuus" - "yearly"). However, in the modern interpretation, clear boundaries are washed away, and an annuity is any regular identical payments (daily, monthly, quarterly, etc.). The two main characteristics of this type of payment are the frequency and the invariance of the amount paid.

However, not all components of an annuity are constant. Take, for example, an agreement concluded with a banking organization. So, when applying for a loan, the borrower undertakes to pay the lender regularly (usually monthly) a certain amount of funds (annuity payments) to repay the loan. This value includes bothpart of the principal amount of the loan, as well as interest on its use. They are the ones that change over time. Initially (until the middle of the loan term) the amount of interest paid exceeds the principal repayment, then (after the middle of the loan term) the situation changes dramatically, and most of the annuity is already the debt of the borrower.

How is the annuity calculated in this case? For a clearer explanation, let's take an example. Suppose a loan agreement is concluded with the following conditions: the loan term is a 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 overpayment on the loan (price of borrowed funds). The payment due on December 28th (and each month thereafter) is calculated based on the formula:

PA_post =R(1 – (1 + i)^{- ) /i, where}

PA_{post – the amount of the loan (or the present value of the annuity, is 150 thousand rubles);}

R – monthly payment amount;

i – monthly interest rate (20%/12=1.67);

n – number of loan periods (12 months).

Thus, R (or annuity) is a value equal to:

PA_posti/(1 – (1 + i)^-)=1500000.0167/(1 - (1 + 0.0167)^{-12)=13898 rubles.}

Now it is easy to determine how much the overpayment on the loan will be with our conditions:

1389812 – 150000=16776.

This is the price you have to pay for using the bank's money. Using the formula in Excel, you can build a table that will list the components of the annuity payment (interest and part of the principal that you will pay every month), recall that they change. It is not difficult to calculate them, just monthly you should reduce the principal debt by the amount already paid and multiply by the interest rate (as you know, it is charged precisely 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 repays the loan, the more the credit institution will earn. That is why banks do not really like it when a loan is repaid ahead of schedule (until recently, in this case, a fee was often charged, which was abolished by law).

This feature of annuity payments (changing components) is typical for loans. Usually, an annuity is just a fixed amount, the payments of which are made at a given frequency. An example of it in other areas: rent, rent, pension, depreciation contributions, regular payments by an insurance organization to policyholders or, conversely, insurance premiums, an annual fee, etc.