If at least once in your life you took a loan, then you came across such concepts as differentiable payment and annuity payment. What is it, what is the difference between them and what is the calculation formula? Learn about all this from the article.
What is a differentiated payment?
The essence of any loan is that a large amount is taken immediately, and is returned over time for parts and with interest. Repayment intervals are standardly set once a month. This monthly amount is called a payment.
Consider it differently. If the amount of debt is divided into equal parts, and the percentage is calculated depending on what is left, then this method of repayment is called a differentiated payment. You can also meet it under the name "classic method", "commercial method" or the method of calculating interest on the balance.
At first glance, it seems that there simply cannot be other repayment options. But this is not so. There are annuity and differentiable payments. The essence of the annuity is that repayment is made every month by the same amount. In order to establish it, interest is calculated for the entire period of using the loan, the amount received is added to the main debt and divided by the number of months.
The disadvantages of differentiated payments
The essence of the disadvantage lies in the very name of the phenomenon - differentiated payment, that is, carried out taking into account the differences. Since the amount of the main debt is divided into equal parts, and interest is calculated depending on the balance, the first payment will be the largest, and the last - the smallest.
Consequently, the borrower will have a particularly difficult time in the first year of payments, but over time the burden on the budget will decrease. This is a drawback for the borrower, but in fact it is impossible to say unequivocally that this is bad. The first year of payments will allow you to discipline and develop the skill to fit into the budget, which in the future can lead to the formation of free money that can be spent on other needs.
Another drawback of such a scheme for the borrower is that the income for obtaining a loan with a similar payment system will require a quarter more. If we are talking about small loans, then this may not be a fundamental factor, but if you think about a mortgage, it can become a significant obstacle to getting approval.
The disadvantage of such a repayment system for the bank is much more serious. A credit institution will receive less interest. Why this happens, you will be able to understand a little later, when we move on to consider the formula and calculation examples. Therefore, banks, especially in the case of mortgages, prefer not to give borrowers a choice, lending only on terms of annuity payments.
The role of inflation
There is another pitfall of such a payment scheme for the borrower, which at first glance does not seem obvious. In long-term lending, part of the monthly payment is slowly consumed by inflation. It's no secret to anyone that 10 thousand rubles now and 10 thousand rubles five years ago are not the same money at all. Whether we like it or not, but the value of money changes over time, this process is especially rapid during a period of economic crisis.
A differentiated load with a gradual decrease in payment does not allow this factor to play in full in favor of the borrower, in contrast to the situation when the repayment occurs in equal parts every month.
Benefits of Differentiable Payments
As already mentioned above, such a payment system will allow less interest to be paid to the bank.The larger the loan size, the greater the savings.
This is more convenient in terms of early repayment. A differentiated loan payment allows you to quickly pay off your main debt. In the first years, most of the payment will go specifically to repay the loan body, unlike annuity payments, when in the first years only interest is paid, and the main debt is reduced minimally. Therefore, if a situation arises that you need to urgently close the debt after several years of repayment, then the loan balance will be significantly lower than in the situation with the annuity.
Even if you partially repay your loan ahead of schedule, this will also save more on interest, because they are charged only on the balance.
Especially good, the benefits will be felt closer to the end of the loan term, as payments become almost imperceptible to the budget, even if you took a large loan to purchase a home.
Differentiated Payment Formula: Main Debt
The payment includes two parts, for the calculation of each of them uses its own formula. The first part is the amount of the principal debt. The second part is the interest that you need to pay for the billing month.
So, the first part is calculated by the formula: B = S / N.
B - the first part of the main payment;
S is the amount of the loan taken;
N is the number of months in the period for which a loan is taken.
Interest calculation formula
Next, you need to calculate the size of percent, for this the following formula is used:
p = Sn * P / 12, where:
p is the amount of accrued interest payable;
Sn is the size of the remaining loan amount;
P - annual interest rate, which is established by the loan agreement.
To calculate the payment, the last step remains, for which you need to use the following formula: b = B + p.
b is the monthly payment amount;
B - the first part of the main payment;
p is the amount of accrued interest.
If you want to calculate what the amount of remaining debt is at a certain point in time, then you need to use the following formula: Sn = S - (B * n), where n is the number of past billing periods.
Differential Payment Calculation Example
Let's calculate the payment amount for the following conditions. The bank took 1,000,000 rubles to buy an apartment. The loan term is 10 years, the rate is 14% per annum.
To make the differential payment calculation, we calculate the first part: 10 years is 120 months. So, 1,000,000 / 120 = 8,333.34 rubles.
We calculate the interest. For the first month it will be 1,000,000 * 14% / 12 = 11,666,66. The payment for the first month will be 20,000 rubles (8,333.34 + 11,666.66).
For the second month, interest will be accrued in the amount of (1,000,000 - 8,333.34) * 14% / 12 = 11,569.44. The payment for the second month will be 19 902.78. As you can see, it has already become smaller, although not by much.
Suppose that a borrower has been paying a loan for a year, what will be his payment after this time? (1,000,000 - 100,000) * 14% / 12 = 10,500 is the amount of interest, therefore, 18,833.34 is the payment. The difference with the payment of the first month is 1,166.66 rubles. The final payment will be 8,430.56 rubles. As you can see, the difference with the payment of the first month is significant.
Let's now calculate the amount of the overpayment on the loan under such conditions. To do this, you need to add together monthly payments for the entire loan period and subtract the loan amount from them. Manually do this for a very long time. For this, it is more convenient to use a differential payments calculator. You can write it yourself using Excel features or calculate on a special site called “Mortgage Calculator”.
In our case, the overpayment on the loan will amount to 705,833 rubles, that is, just over 70%.
An example of calculating an annuity payment
In order to compare what is more profitable on their own, rather than relying on someone else’s allegations, you need to calculate the size of the annuity payment and the overpayment for similar lending conditions.
The calculation formula is quite complicated: x = S * (P / ((1 + P)n - 1);
X - monthly payment
S is the loan amount,
P is 1/12 of the interest rate,
N is the number of months in the crediting period.
In our case (1 000 000 rubles for 10 years at 14% per annum), the monthly payment will be 15 527 rubles, and the amount of overpayment for the whole period - 863 197 rubles, that is, more than 86%. Now you should understand why the bank does not like to offer a differentiated payment, and in the vast majority of cases the borrower does not even have a choice.
From the example, it becomes obvious according to which scheme the load on the family budget will be lower, and it is also clear that for differentiated payments with the same loan amount, the borrower's income should be 25% higher.
Mortgage
It is logical that for consumer lending or even car loans in most cases, the scheme by which payments are calculated does not matter. But if we are talking about a loan for the purchase of housing, then it is already very important what kind of mortgage will be, with differentiated payments or annuity.
Most lending institutions both in the Russian Federation and abroad do not offer a choice, offering only repayment in equal shares. This is due not only to the desire of banks to earn as much as possible, but also to borrowers. Not everyone is happy with the need to pay more in the early years, and not every person has such an income to get the approval of the bank, not everyone likes the fact that it is impossible to accurately plan their expenses.
Therefore, even experienced and well-informed borrowers, having weighed all the arguments, choose repayment in equal parts. Experts write that the demand for loan products with differentiable payments is extremely low, and in the conditions of economic instability it has become even lower.
Therefore, the list of banks providing the choice is extremely short. It includes: Gazprombank, Nordea Bank and Petrocommerce. Previously, Sberbank also provided such an opportunity, now it is no longer there.
