Annuity is the payments that we face everywhere

Today, many are familiar with annuity payments due to the wide spread of this method of repayment of loan obligations. However, an annuity is not just a banking term. It occurs in various spheres - from insurance to pension, in which it is used to designate regular payments / payments. Initially, this word implied an annual periodicity (from the Latin "annuus" - "annually"). However, in modern interpretation, clear boundaries are washed away, and annuity is any regular equal payments (daily, monthly, quarterly, etc.). The two main characteristics of this type of payment are the periodicity and the invariability of the amount paid.

However, not all the components of an annuity are constant values. Take for example an agreement concluded with a banking organization. So, when a loan is issued, the borrower undertakes to pay the lender regularly (as a rule, monthly) a certain amount of money (annuity payments) to repay the loan. In this case, this amount includes both part of the principal amount of the loan, as well as interest for its use. They change in time. Initially (until 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 radically, and most of the annuity is already borrower's debt.

How does the annuity calculation work in this case? For a more understandable explanation, let us give an example. Let's assume that a loan agreement has been concluded with the following conditions: the loan period is a year (from November 28, 2013 to November 28, 2014); Interest rate - 20% per annum; The amount of the loan (principal) is 150 thousand rubles. We are interested in the amount of monthly payments (annuity) and overpayment on the loan (the price of borrowed funds). The payment to be made 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 thousand rubles);

R - the amount of the monthly payment;

I - monthly interest rate (20% / 12 = 1.67);

N - the number of crediting 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 overpayment will be on the loan with our terms:

13898 * 12 - 150000 = 16776.

This price will have to be paid for using the bank's money. Using the formula in Excel, you can build a tablet in which the components of the annuity payment (interest and part of the principal debt that you will pay each month) will be also recorded, recall that they change. Calculate them easily, just monthly should reduce the main debt by the amount already paid and multiply by the interest rate (it, as is known, is charged on the balance of the debt).

Of course, the annuity method brings a significant benefit to the bank, because initially the borrower pays mainly interest, and only then repayment of the principal amount begins. And the longer the client pays the loan, the more the credit organization will earn. That is why banks do not like very much when a loan is repaid ahead of schedule (until recently, in this case, a commission was often charged, which was abolished 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 at a given periodicity. His example in other areas: rent, rent, pension, amortization fees, regular payments to the insurance organization to policyholders or, on the contrary, insurance premiums, annual fee, etc.