Annuity is a term that has several different meanings. In its broadest interpretation, it can be represented as a tool that serves to carry out financial activities.
Multiple Annuity Values
For example, the first meaning that the concept of annuity has is one of the types of government loans, and urgent ones. Such loans can be placed under the condition that interest will be paid annually and a certain part of the loan will be repaid.
At the same time, annuity is cash payments equal to each other and paid in repayment of loan obligations and interest on it. Such payments are made after a certain time period.
Annuity concept
Consider the concept of annuity in more detail.
An annuity, or, as it is also called, financial annuity, is a generalized term describing the schedule according to which a financial instrument is repaid, and the term annuity implies the payment of not only a certain part of the principal debt, but also payment of interest - interest for its use. The main feature of the annuity is that payments in this case are equal to each other and are made at absolutely equal time intervals. The annuity schedule is quite complicated. It differs significantly from the schedule, which reflects the payment of the due amount in full and at the end of the period during which the instrument was in operation, and from the schedule, which reflects the periodic payment of only interest and the process of repayment of the amount to the main debt at the end of the instrument. There is a special annuity formula. We give it below.
Thus, it can be established that the annuity type payment in its structure consists of two parts: the part reflecting the main debt, and the part reflecting the remuneration for the use of credit funds.
Annuity Examples
In the most general sense, an annuity can be understood not only as an instrument of a financial nature, but also the actual amount of payment, which has a certain periodicity, and the type of schedule that reflects the repayment process.
- An annuity is a state urgent loan of a certain type, according to which there is an annual payment of a certain part of the main debt and interest for using the loan itself.
- Equal cash payments, the payment of which is expected at equal time intervals. Moreover, such payments include the amount used to pay off part of the principal debt, and the amount used to pay interest.
- The concept of annuity is also used in insurance, in particular, in life insurance. In this case, it means an agreement that an individual concludes with an insurance company. Such an agreement gives an individual the right to receive regular payments upon the arrival of a previously agreed time. For example, after retirement.
- The annuity schedule can also be used to accumulate a given amount of money at a certain point. In this case, equivalent deposits are supposed to be made to the deposit account, on which interest is accrued.
Types of Annuities
Annuities can be classified into two types, depending on the time when the first payment is paid:
- If the payment is made at the end of the first period, then such an annuity is called postnumerando.
- If payment is made at the very beginning of the first period, then such annuity is called prenumerando.
Still, most often, annuity is a certain way of repaying loan funds. Therefore, in this article we focus on this very meaning of this concept.
Today, only a small part of Russian banks prefer to use a different loan repayment scheme. Using the annuity method allows the bank to receive a guaranteed profit. This is due to the fact that the annuity schedule is structured in such a way that the bank is first returned interest on the use of credit funds, and only then the credit body is paid, that is, the amount of the principal debt.
Annuity formula
The formula by which the annuity is calculated is quite complicated. Her record has various representations.
One of them: PI = (S * pr / 12) / (1 - 1 / (1 + pr / 12) N), in this formula:
- Pl - represents the annuity payment itself.
- S - the total amount of loan funds.
- Pr is the interest rate or annuity ratio used on the loan.
- N is the total number of periods during which repayment will be made (months are most often used).
Her functions
It should be noted that throughout the entire period the size of the payment does not change, but its structure is significantly different from the structure of another, the same payment. The payment made in the first month of repayment mainly consists of the amount of interest, and payments made by the end of the payment period mainly consist of the amount used to repay the loan. This is how cash flows are managed.
In order to determine which structure a certain payment has, it makes sense to use this particular formula. It clearly reflects the percentage that is included in it. To make this calculation, you need to take the balance of the principal debt and multiply it by 1/12 of the annual loan rate.
An example that clearly reflects the way annuity is calculated
The formula that we presented above will be much clearer if we put it into practice, having examined the corresponding example.
Suppose a client of a bank draws up a loan. The loan amount is one hundred thousand rubles, the loan term is 12 months, the interest rate on the loan in this case is 24 percent per annum. In accordance with the formula, you can calculate what the current value of the annuity will be:
(100000 * 0,24/12)/(1 - 1)/(1 + 0,24/12) 12 = 2000/0,2115 = 9457.
Thus, it is precisely this amount, in the amount of 9457 rubles, that the client will have to transfer each month to the bank in order to repay the loan taken.
Next, let's try to calculate the interest rate for the very first payment on this loan:
100000 * 0,24/12 = 2000.
It turns out that as part of the first payment of 9457 rubles, only 2,000 rubles will go towards paying interest on the loan. Accordingly, the amount of 7457 will go towards repayment of the main debt.
After the first payment is made, the total debt will decrease and amount to 92543 rubles:
100000 - 7457 = 92543.
From this amount, you can calculate the percentage for the next, second, loan payment:
92543 * 0,24/12 = 1851.
So, the second payment includes interest in the amount of 1851 rubles and the main debt of 5606 rubles.
It is in this way that calculation is made for each payment for the entire loan term.
Automatic Payment Calculation Method
Undoubtedly, making such calculations is rather laborious. The formula for calculating an annuity can only be useful in order to understand the principles of its calculation. With regard to practice, it does not make sense to count payments using a calculator. Modern technologies make it possible to automate the calculation process without problems, which makes the cash flow management process easier.
When a client draws up a loan at a bank, then specially for him the employee of the credit organization will make a printout reflecting all the data of the annuity schedule.It will reflect all the necessary data: the amount of payment, dates when payments should be made, as well as the structure of the payment, reflecting the amount of interest and the principal amount for each payment.
In addition, on the Internet you can find a special calculator. It will be enough to enter in the appropriate fields such data as the total loan amount, its term, rate. After that, the calculator will instantly make the corresponding annuity calculation and display all the information of interest: the amount of payment that will have to be paid every month, and an approximate schedule for repaying the loan.
A similar calculation allows you to make such an office program as Excel. This program provides a function called PMT - it will help calculate the size of the annuity. But, unfortunately, with this method of calculation, you can not get an approximate repayment schedule.
Annuity Pros
The annuity method is not always beneficial for the client, although it is convenient. When using the annuity, there will be no confusion with the size of the payment and the term for making it, because the annuity always has a fixed amount of payments that must be paid monthly. This method will avoid the need to contact the bank every month in order for its employees to calculate the next payment.
A similar method is convenient if the borrower has a low income.
An alternative scheme, called differential, involves a monthly recalculation of the payment amount. This has to be done because with such a scheme each month there is a decrease in the amount of the main debt, respectively, and interest for using a smaller amount has to be paid less. That is, each subsequent payment will be less than the previous one. However, the first payments under this scheme are very high, and not every borrower can afford it.
Annuity Disadvantages
During the first half of the period for which a loan is issued, the payment in its structure contains mainly interest. That is why the annuity scheme is very beneficial for banks. It is best to make repayments of the loan ahead of schedule precisely in the first half of the term, since then this does not make practical sense, since most of the interest has already been paid. Repayment of the loan ahead of schedule in the second half of the term will not bring any benefit to the borrower, since the funds contributed to repay interest on the loan will not be returned.
Annuity indicators
In the event that the annuity is considered from the point of view of the creditor, and not the borrower, it is necessary to evaluate payments in order to analyze receipts.
Few people may find it useful to assess this kind of everyday life. However, when analyzing and comparing current costs and cash receipts that will occur in the future, they are necessary.
There are two main indicators by which an annuity is evaluated. This cost is modern and future.
The future value of an annuity is the sum of absolutely all the elements that make up the annuity. This also includes interest that accrues at the end of the term. Elements, or, as they are also called, members of an annuity, are precisely these equal payments.
This indicator can be used if it is necessary to calculate the amount of the deposit (replenished), which can be accumulated by a certain time, if a regular contribution of funds is made at a certain interest rate.
Modern (current) value is a set of annuity elements that are reduced at the time when it was launched. This indicator is used to assess the feasibility of investing in a certain contribution, which should bring a constant and regular income. That is, this estimate allows you to calculate whether future earnings will be higher than the price of the asset itself.
By the way, this assessment can also be used to evaluate what will be more profitable - to make a purchase on credit or to pay for it immediately.