Calculation of annuity payments on a loan: an example

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

The first rule when applying for a loan is to adequately assess your own solvency so that payments on it do not become burdensome for the borrower over time. But at this stage, difficulties sometimes arise, since not everyone has an economic education in order to correctly make the necessary calculations. To facilitate the task, all possible methods for calculating annuity payments on a loan are collected here, which you can use to plan your own budget.

Annuity payment is…

Before the practical part of studying the issue, you should familiarize yourself with the theory. In economic theory, an annuity payment is one of the ways to make a monthly payment on a loan, when its amount remains unchanged throughout the entire loan term.

With this method of loan repayment, the payer simultaneously pays both the accrued interest and part of the principal amount. But, as a rule, at the beginning, the monthly installment mainly consists of interest on the loan. Therefore, when calculating annuity payments on a loan, you may notice that this method of repayment is not very beneficial for borrowers.

Annuity classification

Depending on additional lending conditions, annuity payments are divided into small groups. Their classification is quite diverse, however, some types of annuities are no longer found or are extremely rare in the list of banking services.

Types of annuities:

• Fixed - unchanged throughout the loan term.
• Currency - the amount of payment may vary depending on fluctuations in the foreign exchange market.
• Indexed - can be adjusted for the current inflation rate.
• Variable - payments vary depending on the level of profitability of the financial instrument.

The mechanism for calculating annuity payments on a loan depends on their type. However, fixed annuities are most commonly used for consumer lending.

Advantages and disadvantages of annuity payments

The calculation of annuity payments on a loan is usually made before its execution. Therefore, it is important to know whether it is worth doing any calculations at all, or whether it is better to immediately choose another bank for obtaining a loan. To decideyou need to weigh all the pros and cons of annuity payments.

Benefits:

• constancy of the amount and date of payment throughout the entire loan term;
• availability for almost all borrowers, regardless of their financial situation;
• possibility of lowering the payment adjusted for inflation.

For many people, the annuity method of repaying a loan is convenient because, knowing the exact amount of the monthly installment, it is easier to plan a family budget. However, in terms of economic benefits, it has several significant drawbacks.

Flaws:

• the total overpayment is much higher than with the differentiated debt repayment method;
• difficulty of early repayment;
• impossibility of recalculation if the borrower wishes to repay the loan ahead of schedule.

If we consider an example of calculating an annuity payment on a loan, it immediately becomes clear that it is profitable for banks to issue such loans to customers. However, some are not so chasing profits, so they provide borrowers with more favorable lending conditions. It should be noted that there are no such companies among microfinance organizations. Therefore, when applying for a loan, the annuity method of repaying the debt is always used.

What does the loan payment consist of?

If we consider the components of an annuity payment, you will notice that it is divided into two parts. The first is fixed interest on the loan, the second is a part of the principal amount. Moreover, the amount of accrued interest usually exceeds the amount going toloan repayment.

The body of the loan is compared with the interest on it only in the middle of the total loan term. Further, the amount that goes to repay the principal debt begins to grow, gradually exceeding the amount of payments for using the loan. As mentioned earlier, this is not beneficial for borrowers, especially when it comes to long-term lending.

Methods for calculating the monthly annuity loan payment

In fact, calculating the exact amount of payment is quite simple. And this can be done in several ways at once. Using at least one of them, you can navigate the upcoming payments and evaluate how "lifting" the bank loan will be.

Methods of calculating the annuity payment:

• manually using the formula;
• using Microsoft Excel;
• on the bank's website using a loan calculator.

Each of the calculation methods, when properly applied, will give an exact figure equal to the upcoming payment amount. Therefore, if there are doubts about the correctness of the calculations already made, you can check by calculating the annuity payment in another possible way.

Calculation formula

Calculation of interest on a loan for annuity payments, regardless of the chosen calculation method, is performed using a special formula. Loan calculators, mobile applications and other software makescorrect calculations, starting from it.

The general form of this formula is as follows:

AP=Ops / 1 - (1 + ps)-c, where:

AP - monthly annuity payment;

O – principal amount;

ps - monthly interest rate of the bank;

s - the number of months in the loan term.

Knowing the formula, you can easily make the necessary calculations yourself. It is enough just to substitute the initial data of the proposed loan instead of letters, and make the necessary mathematical calculations using a conventional calculator. But to make the calculation of loan repayment by annuity payments the most understandable, let's look at an example.

Calculation example

Suppose that the borrower took a loan from the bank in the amount of 50,000 rubles for a period of 5 years. Under the terms of the loan agreement, the annual interest rate on the loan is 20%.

Based on the formula, you need to know the monthly interest rate for calculations. Banks rarely indicate this figure in the loan agreement, so you need to find it yourself. To do this, use the formula:

ps=P / 100 / 12, where:

P is the annual interest rate.

Calculation:

ps=20 / 100 / 12=0, 017.

Knowing all the initial data, you can start finding an annuity loan payment. It looks like this:

AP=50,0000.017 / 1 - (1 + 0.017)-60=1336.47 rubles

Calculationannuity payments on a loan in Excel

Excel is not just a big spreadsheet. In it, you can perform a huge number of calculations, knowing only which formulas to use. To calculate the annuity payment in Excel, there is a special function - PMT. To use it correctly, you need to act by adhering to the following steps:

1. Fill in the initial data (amount, interest and term of the loan in cells B2, B3, B4, respectively).
2. Make a loan repayment schedule by months (A7 -A _).
3. Make a Loan Payments column (B7 - B _).
4. In front of the first month in the column "Payments on the loan" enter the formula

=PMT ($B3/12;$B$4;$B$2) and press Enter.

The result of the calculation will be displayed in the table in red with a "-" sign. This is normal, because the borrower will give this money to the bank, and not receive it. The formula for calculating a loan with annuity payments in Excel allows you to make calculations in such a way that the values \u200b\u200bare positive. With its help, bank employees can make and print a payment schedule for borrowers in a matter of minutes, saving them time.

To fill in all the months, you need to stretch the cell with the formula to the end of the repayment schedule. But since the annuity payment does not change over time, the numbers in the cells will be the same.

You can double-check the received data using a creditannuity payment calculator. It is available on the websites of all banks that issue loans with this method of repayment. To use the loan calculator, you will need the same initial data as for the previous calculation methods. They must be entered in the fields provided. And then the program will independently make all the calculations within a few seconds, giving the potential borrower the opportunity to evaluate the amount received and think carefully about the upcoming loan.