Greetings! I am sure that I do not have to know and be able to do everything in the world. Yes, this is impossible in principle. But in the most important areas for a person it is worth navigating at least at the “teapot” level.

I consider work, business, family, health and, of course, money to be vital areas. What am I getting at? Moreover, any investment requires. Even if it’s a banal bank deposit or a loan for business development.

To be honest, I haven’t done such calculations manually for a very long time. For what? After all, there are a lot of convenient applications and online calculators. As a last resort, a “fail-safe” Excel table will help out.

But it doesn’t hurt to know the elementary formulas for basic calculations! Agree, interest on deposits or loans can definitely be classified as “basic”.

Below we will recall school algebra. It must be useful at least somewhere in life.

We calculate the percentage of the deposit amount

Let me remind you that interest on a bank deposit can be simple or complex.

In the first case, the bank accrues income on the initial deposit amount. That is, every month/quarter/year the depositor receives the same “bonus” from the bank.

Of course, the calculation formulas for simple and compound interest are different.

Let's look at them using a specific example.

Return on deposit with simple interest

• Amount % = (deposit*rate*days in the billing period)/(days in the year*100)

Example. Valera opened a deposit in the amount of 20,000 rubles at 9% per annum for one year.

We will calculate the profitability of the deposit for a year, month, week and one day.

Interest amount for the year = (20,000*9*365)/(365*100) = 1800 rubles

It is clear that in our example, the annual profitability could be calculated much more simply: 20,000 * 0.09. And as a result, you get the same 1800 rubles. But since we decided to count according to the formula, then we will count according to it. The main thing is to understand the logic.

Interest amount for the month (June) = (20,000*9*30)/(365*100) = 148 rubles

Amount of interest for the week = (20,000*9*7)/(365*100) = 34.5 rubles

Amount of interest per day = (20,000*9*1)/(365*100) = 5 rubles

Agree, the simple interest formula is elementary. It allows you to calculate the return on a deposit for any number of days.

Return on deposit with compound interest

Let's complicate the example. The formula for calculating compound interest is a little more sophisticated than in the previous version. The calculator must have a power function. Alternatively, you can use the degree option in the Excel table.

• Amount % = contribution * (1+ rate for the capitalization period) number of capitalizations - contribution
• Rate for the capitalization period = (annual rate*days in the capitalization period)/(number of days in a year*100)

Let's return to our example. Valera placed the same 20,000 rubles on a bank deposit at 9% per annum. But this time - .

First, let's calculate the rate for the capitalization period. According to the terms of the deposit, interest is accrued and “added” to the deposit once a month. This means that we have 30 days in the capitalization period.

Thus, the rate for the capitalization period = (9*30)/(365*100) = 0.0074%

Now we calculate how much our contribution will bring in the form of interest for different periods.

Interest amount for the year = 20,000*(1+0.0074) 12 – 20,000 = 1,850 rubles

We raise it to the power of “12” because the year includes twelve periods of capitalization.

As you can see, even with such a symbolic amount and a short period of time, the difference in the profitability of a deposit with simple and compound interest is 50 rubles.

Interest amount for six months = 20,000*(1+0.0074) 6 – 20,000 = 905 rubles

Interest amount for the quarter = 20,000*(1+0.0074) 3 – 20,000 = 447 rubles

Monthly interest amount = 20,000*(1+0.0074) 1 – 20,000 = 148 rubles

Note! Capitalization of interest does not in any way affect the profitability of the deposit for the first month.

The investor will receive the same 148 rubles with both simple and compound interest. Differences in profitability will begin from the second month. And the longer the deposit term, the more significant the difference will be.

Before we stray too far from the topic of compound interest, let's check how fair one of the recommendations of financial advisors is. I mean the advice to choose not once every six months or quarter, but once a month.

Suppose our conditional Valera placed a deposit for the same amount, term and at the same rate, but with interest capitalized every six months.

Rate = (9*182)/(365*100) = 0.0449%

Now we calculate the return on the deposit for the year.

Interest amount for the year = 20,000*(1+0.0449) 2 – 20,000 = 1,836 rubles

Conclusion: all other things being equal, semi-annual capitalization will bring Valera 14 rubles less than monthly capitalization (1850 - 1836).

I understand that the difference is very small. But our other initial data is symbolic. For large amounts and long periods, 14 rubles will turn into thousands and millions.

We calculate the percentage of the loan

We move from deposits to loans. In fact, the loan calculation formula is no different from the basic one.

Example. Yuri took out a consumer loan from Sberbank in the amount of 100,000 rubles for 2 years at 20% per annum.

• Amount % = (debt balance*annual rate*days in the billing period)/(number of days in a year*100)

Interest amount for the first month = (100000*20*30)/(365*100) = 1644 rubles

Amount of interest for one day = (100000*20*1)/(365*100) = 55 rubles

Note! Along with the balance of debt, the amount of interest on the loan decreases. In this regard, the differentiated scheme is much “fair” than the annuity scheme.

Now suppose our Yuri has repaid half of his loan. And now the balance of his debt to the bank is not 100,000, but 50,000 rubles.

How much will his interest burden decrease?

Monthly interest amount = (50,000*20*30)/(365*100) = 822 rubles (instead of 1644)

Amount of interest for one day = (50,000*20*1)/(365*100) = 27 rubles (instead of 55)

Everything is fair: the debt to the bank has decreased by half - the “interest” burden on the borrower has decreased by half.

Do you calculate interest on loans and deposits for yourself? Subscribe to updates and share links to fresh posts with your friends on social networks!

Loans have already fit so well into our lives today that many simply cannot do without them. However, not all of our compatriots can calculate in advance the amount of overpayment on the requested loan and choose the bank with the most attractive conditions for issuing borrowed funds.

Experts recommend carefully studying the terms of the loan agreement (many lending institutions provide for the issuance of standard agreements for preliminary review). After finding out the main parameters of the loan transaction, you should calculate the amount of interest that you will have to pay on the loan for the entire loan term - the actual amount of the overpayment.

Mechanism for calculating the actual amount of interest on a loan

Let's assume that you know the amount of loan funds, the interest rate and the expected loan term (in days), for example:

• the amount of the planned loan is 100 thousand rubles;
• interest rate – 18%;
• loan term – 1 year, i.e. 365 days (excluding leap years).

Then we get the following calculation:

• Find the amount of interest for one day of using borrowed funds.

100,000 rubles * 18% / 365 days = 49.32 rubles.

• We calculate the amount of interest for one month.

RUB 49.32 * 30 days = 1,479.60 rub.

• We calculate the amount of overpayment on interest for the entire loan period.

RUB 1,479.60 *12 months = 17,755.20 rubles.

If you are interested in the total amount that you will have to pay on the loan monthly, then:

• We estimate the amount of the principal debt (if a differentiated repayment method is chosen):

100,000 rub. / 12 months = 8,333.33 rub.

• Find the monthly payment amount taking into account accrued interest:

8,333.33 + 1,479.60 = 9,812.93 rubles.

To get a real picture of upcoming payments on the requested loan, you can use a schedule compiled independently in Microsoft Excel. We create a table in a new file with five columns: months, loan balance, interest, principal payment amount and total amount due.

We enter the expected months of lending in the first column. In the “Loan balance” column we indicate the amount of the loan issued. We enter formulas in the cells where the loan balance will be displayed every month:

Debt amount = Loan balance for last month – Principal payment amount for the current month.

Enter the formulas for calculating the amount of interest in the corresponding column:

(Principal balance * Interest rate * Number of daysper month)/(365 *100)

By adding up the interest received for the entire expected loan period using the “AutoSum” function, we get the total amount of overpayment on interest.

For clients who have not yet mastered a computer, there is a “Loan Calculator” service on the official websites of most operating banks. It is enough to enter the key parameters of the loan there (amount and term), and you will find out whether it is profitable to enter into a loan deal with this lender.

According to the differentiated schedule, the loan payment amount will decrease with each subsequent month due to a decrease in the amount of interest paid. However, finding a bank that provides such a repayment system is almost impossible in our time, since the vast majority of credit institutions in Russia have switched to the annuity method of charging interest.

Remember that you should not “buy” into the tempting offers of some organizations to obtain an interest-free loan. Most likely, they simply forgot to warn you about the additional services provided by the loan program. In this case, be prepared to pay much more for the loan than was originally stated.

Site search

One of the main parameters of a banking product that affects the ability and desire of a potential borrower to obtain a loan is the interest rate. It's simple - the higher it is, the more you will have to pay on the loan. The formula for calculating interest on a loan must be known to the bank client himself. This will allow you to independently carry out calculations and determine how profitable it is to use a loan from a particular financial institution.

What affects the loan rate?

A potential client, in addition to the interest rate, should also pay attention to the associated costs that he will incur when completing the transaction and the amount of commissions. These costs can significantly increase, and as a result it turns out that taking out a loan from another bank at a higher rate would be more profitable.

The amount of the debtor's periodic contribution depends on the size of the rate. But in order for the client to save, he needs to know what affects the amount of interest accrued. This value is directly influenced by:

• debt balance - the lower it is, the less interest you need to pay, which means the borrower should be interested in repaying the loan as quickly as possible;
• the number of calendar days in a month - the more there are, the greater the accrued interest will be. So, in a month with 31 days, their amount will be greater than in a 30-day month. The formula for calculating a loan can clearly confirm this - after all, in it the number of days of the month is in the numerator of the fraction.
• the number of calendar days in a year - the larger it is, the smaller the next installment will be. All banks in their loan agreements indicate the number of days, which is the basis for calculating accrued interest - this can be the actual number of days in the calendar, or it can be a fixed number, usually 360;
• the date of repayment of the principal debt - the closer it is to the first day of the month, the less interest will be accrued in the next month, since the debt will decrease faster.

Types of repayment schedules

Financial institutions in their practice use two ways to calculate the monthly loan installment.

The classic (or standard) is based on the periodic repayment of the debt in equal parts, interest is calculated on the balance of the debt according to a simple formula.

The formula for simple interest on loans is as follows:

К*n*%/360 or 365(6), where

K – debt balance;

n – number of calendar days in a month;

% – debt rate divided by 100;

360 or 365(6) – the number of calendar days in a year, which is specified in the loan agreement.

With this schedule, the monthly payment amount is constantly decreasing.

The formula for an annuity loan payment is somewhat more complicated:

Р=(К*%/12) /(1-(1+%/12) -n), where

P – monthly payment;

n – contract duration in months;

% - bid;

K – initial loan amount.

When using this payment method, the debtor deposits equal amounts into the bank's cash desk throughout the entire loan period.

Calculation example

• loan amount – 200 thousand rubles;
• loan term – 2 years;
• rate – 22.5% per annum.

There are two options for calculation: using a loan calculator, which is available on the website of almost every bank, or making a simple table in Excel.

So, the repayment schedule according to the standard scheme will look like this:

Period	Main debt	Payment of principal	Payout,%	Payment
1	200 000.00	8 333.33	3 750.00	12 083.33
2	191 666.67	8 333.33	3 593.75	11 927.08
3	183 333.33	8 333.33	3 437.50	11 770.83
4	175 000.00	8 333.33	3 281.25	11 614.58
5	166 666.67	8 333.33	3 125.00	11 458.33
6	158 333.33	8 333.33	2 968.75	11 302.08
7	150 000.00	8 333.33	2 812.50	11 145.83
8	141 666.67	8 333.33	2 656.25	10 989.58
9	133 333.33	8 333.33	2 500.00	10 833.33
10	125 000.00	8 333.33	2 343.75	10 677.08
11	116 666.67	8 333.33	2 187.50	10 520.83
12	108 333.33	8 333.33	2 031.25	10 364.58
13	100 000.00	8 333.33	1 875.00	10 208.33
14	91 666.67	8 333.33	1 718.75	10 052.08
15	83 333.33	8 333.33	1 562.50	9 895.83
16	75 000.00	8 333.33	1 406.25	9 739.58
17	66 666.67	8 333.33	1 250.00	9 583.33
18	58 333.33	8 333.33	1 093.75	9 427.08
19	50 000.00	8 333.33	937.50	9 270.83
20	41 666.67	8 333.33	781.25	9 114.58
21	33 333.33	8 333.33	625.00	8 958.33
22	25 000.00	8 333.33	468.75	8 802.08
23	16 666.67	8 333.33	312.50	8 645.83
24	8 333.33	8 333.33	156.25	8 489.58

As you can see, the approximate overpayment for the entire period of using the loan is about 46,875 rubles, and it may be less if you pay off the debt ahead of schedule: in this case, the borrower will pay interest for the actual days of using the borrowed money.

Formula for calculating a loan with an example of using an annuity repayment schedule and the same transaction parameters:

Period	Main debt	Payment of principal	Pay,%	Payment
1	200 000.00	6 675.08	3 750.00	10 425.08
2	193 324.92	6 800.24	3 624.84	10 425.08
3	186 524.68	6 927.74	3 497.34	10 425.08
4	179 596.94	7 057.64	3 367.44	10 425.08
5	172 539.30	7 189.97	3 235.11	10 425.08
6	165 349.33	7 324.78	3 100.30	10 425.08
7	158 024.55	7 462.12	2 962.96	10 425.08
8	150 562.44	7 602.03	2 823.05	10 425.08
9	142 960.40	7 744.57	2 680.51	10 425.08
10	135 215.83	7 889.78	2 535.30	10 425.08
11	127 326.05	8 037.72	2 387.36	10 425.08
12	119 288.33	8 188.42	2 236.66	10 425.08
13	111 099.90	8 341.96	2 083.12	10 425.08
14	102 757.95	8 498.37	1 926.71	10 425.08
15	94 259.58	8 657.71	1 767.37	10 425.08
16	85 601.87	8 820.04	1 605.04	10 425.08
17	76 781.82	8 985.42	1 439.66	10 425.08
18	67 796.40	9 153.90	1 271.18	10 425.08
19	58 642.50	9 325.53	1 099.55	10 425.08
20	49 316.97	9 500.39	924.69	10 425.08
21	39 816.58	9 678.52	746.56	10 425.08
22	30 138.06	9 859.99	565.09	10 425.08
23	20 278.07	10 044.87	380.21	10 425.08
24	10 233.21	10 233.21	191.87	10 425.08

In this case, the overpayment on the debt is larger, it is approximately 50,202 rubles, but at the same time, the initial monthly payments are smaller, which gives the borrower more opportunities to repay the loan.

Knowing the basic formulas for calculating loan payments, the borrower can use this data to reduce the overall overpayment and save a certain amount.

Loan calculation in Excel: Video

Today, borrowing money to buy a car, real estate, or just an expensive item is becoming more and more popular, and of course, before going to the bank or the office of a microloan company (you never know), I would like to know how to calculate a loan and, accordingly, understand how much will have to be deducted from your salary to pay the loan amount and interest on it. By the way, there is nothing complicated about this - you can calculate loan payments in two ways:

1. via loan calculator
2. independently according to the formula

The first method is probably suitable for you at the moment, but it is also advisable to know the second, even if you are not an economics student.

How to calculate a loan online using a calculator

So, the first and easiest way to make all the calculations is to enter the initial parameters of the proposed loan into the calculator presented below:

By the way, I already used it in the article ““, but I will repeat the main points:

• annuity payments are a method of paying the loan body and interest on it in equal installments (resulting in the same monthly installment). With this payment method, overpayments are usually higher, although there are exceptions to this rule.
• differentiated payments - in this case, the monthly payment decreases after each next installment, since only the body of the loan is paid in equal parts, and interest is charged on the balance.
• it is possible to calculate the loan amount based on the income level and capabilities of the borrower
• The calculator allows you to make calculations for any type of loan: consumer, mortgage, car, etc. It doesn’t matter which bank you want to contact: Sberbank, VTB 24 or Home Credit (by the way, I have an article ““, but there is no similar one about loans yet).
• If you want a more complex calculator that would take into account, for example, the bank’s commission for maintaining a loan, I recommend turning to the article indicated at the beginning of the paragraph and looking at a selection of serious calculators.

Formulas for manual calculations

If for some reason you want to know on what formulas this service works, I’ll post them below with explanations.

The annuity payment formula is as follows:

source banki.ru

however, if there is a fee for maintaining an account, it must also be added to the monthly payments.
Let me give you an example. Let's say we borrow a product worth 20,000 rubles for 1 year (12 months) at 24% per annum with an initial payment of 10%. How to calculate the loan in this case? Very interesting. We get:

• The first payment will be 2,000 rubles (20,000 * 10%)
• The loan amount will become equal to c = 20,000 -minus 2,000 = 18,000 rubles
• The denominator of the progression in this case will be: a = 1 + 24/1200 = 1.02
• Based on this, the monthly payment coefficient will be: k = 1.02^12[in 12th century]*(1.02 - 1)/(1.02[in 12th century]^12 - 1) = 1.26824*0 .02/0.26824 = 0.0945 (reduced the decimal places a little)
• Total, the monthly payment will be: s_m = k*c = 0.0945 * 18,000 = 1,701 rubles

The second case is to calculate the monthly payment for a differentiated payment repayment scheme. Oddly enough, but it is calculated more simply:
The monthly payment for a certain month (for example, for month i, where i is a positive integer) is calculated using the formula:
sum(i)=d+pr(i),
where d is the contribution to repay the principal debt (loan body), calculated using the formula d=sum/N (sum is the amount of the principal debt, N is the number of months for which the loan was taken),
рr(i) - interest accrued for using the loan in the i-th month and calculated according to the formula:
pr(i)=(sum-d*(i-1))*p/1200, where in this case p is the annual loan rate.
Example: we take a loan of 100,000 rubles (sum) for 24 months (N) with an interest rate of 20% per annum (p).
Let’s assume that the commission for opening a loan account is 1% and is charged once at the very beginning.
Based on these conditions, we will calculate how much you need to pay each month and how much we will pay in the form of commissions.
Solution:
d=sum/N = 100,000/24 ​​= 4166.7 rubles - we will pay every month towards the principal debt (100,000 rubles).
Let's look at the amount of contributions including interest:

1. 1 month: pr(1)=(100,000-4166.7*(1-1)) *smart. 20/1200 = 100,000*0.0166 = 1666.7 rubles (for interest in the first month)
2. sum(1) = d+pr(1)=4166.7+1666.7=5833.4 (total to be paid in the first month)
3. 2nd month: pr(2)=(100,000-4166.7(2-1)) *smart. 20/1200 = 95,833.3*0.0166 = 1597.2 rubles
4. sum(2) = d+pr(2)=4166.7+1597.2=5763.9 rubles (to be paid in the second month)

and so on until the end of the loan term.
You can calculate the fee for using a loan as follows:
p_k=p*(N+1)/24
here p is the loan interest rate (annual), N is the number of months for which the loan was taken
It turns out that p_k in this case is equal to: p_k = 20* (24+1)/24=20.8%
In total, it turns out that the borrower will overpay on the loan 20.8% + 1% (opening fee) = 21.8%
Calculating a loan turned out to be very difficult, but exciting.

I hope now you understand too, how to calculate a bank loan or simply with microcredit. If you have questions, ask in the comments. For the work done, please retweet and +1.

Zapsibkombank, like most modern financial institutions in Russia, provides its clients with a ready-made calculator for calculating monthly loan payments, which uses several standard formulas for calculations.

Nevertheless, it is beneficial for any consumer to know and be able to independently recalculate the interest on the loan. After all, in this way the client has the opportunity to verify the correctness of the numbers that are so important to him.

Positioning itself as an honest, transparent financial structure that works exclusively for the benefit of clients, Zapsibcombank provides you with information that allows you to understand in detail all the nuances of lending. We will teach you how to quickly calculate your monthly payment when using a loan.

How to independently cope with the calculation of interest on a loan?

When planning to take out a loan from the Bank, you must initially correctly calculate your own strengths. It is important to remember that the amount of money you overpay for using a loan directly depends on the rate of debt repayment. In other words, the faster you are able to repay the loan, the lower the total amount of interest accrued by the Bank will be.

To find out the correct calculated amount of interest on the loan, you must consider the following data:

• The amount (amount) of the loan received;
• Amount of annual interest rate;
• Selected type of debt repayment: annuity or differentiated loan payment system;
• Planned number of days to use the loan.

Important!

A differentiated loan payment system is a system in which the monthly loan payment is constantly decreasing, since the generated payment consists of a certain share of the loan body and interest accrued strictly on the remaining amount.

The annuity system of loan payments is characterized by the uniformity of monthly payments. In this case, a fixed monthly payment is made up of a certain (changing) share of the loan body and interest that is accrued for the use of the money received.

It is quite clear that the calculation of interest on a loan will be slightly different for different repayment systems.

Calculation of interest on a loan subject to the choice of a differentiated payment system

The monthly payment under a differentiated loan repayment system usually consists of two parts:

• A fixed amount that allows you to repay the loan in equal parts;
• A constantly decreasing part, representing the amount of interest accrued on the loan balance.

The fixed monthly principal repayment amount is calculated by dividing the loan amount by 12 months. Further, to calculate monthly interest, the system of differentiated loan payments involves the use of a simple interest formula.

SNP=(OOZ×PS×KDM)/(100×365),

where the amount of accrued interest (SNP) is equal to the quotient of the numbers obtained by multiplying the balance of the principal loan (PLO), the interest rate (IR), the number of days in the selected month (KDM) and the product of one hundred percent and the number of days in the year (365 or 366).

Since the amount of the principal debt will constantly decrease by the amount of the previously paid base part of the loan, the amount of interest accrued by the bank will also decrease monthly.

For example, a client was given a loan of 48,000 rubles for one year with a differentiated debt repayment system at 10% per annum. The fixed amount of repayment of the principal amount of the loan will be 4,000 rubles (48,000/12=4000). In this case, the monthly loan amount will decrease by exactly 4,000.

In the first month, the client’s payment will be – 4,000 (repayment of the loan principal) + 407.67 (48,000*10*31/100*365)=4,407.67. In the second month – 4,000 + 361.64 (44,000*10*30/100*365) = 4,361.64. Third month – 4,000 +339.73 (40,000*10*31/100*365) 4,339.73 and so on.

Calculation of interest on a loan subject to choosing an annuity payment system

Annuity is the name given to the system of repaying debt in equal installments. In other words, with an annuity loan repayment system, monthly payments do not change during the entire period of using the loan.

The monthly payment under such a loan repayment system also includes two components:

• The amount of interest for using the loan;
• A certain portion of the loan body.

The classic formula for calculating interest on a loan with an annuity repayment system is as follows:

SEP=(PSK ×GPS/12)/(1-〖(1/(1+G PS⁄12))〗^(KP-1)),

where SEP is the amount of the monthly payment;

PSK – primary loan amount;

APR – annual interest rate;

KP – the planned number of loan payments for the entire period of using the loan.

For example, a client was provided with a loan of 48,000 rubles for one year with an annuity system of debt repayment at 10% per annum. The monthly payment amount (SEP), in this case, will be:

What is more profitable: annuity or differentiated repayment?

Each loan payment system has certain advantages and disadvantages. That is why the client always has to choose a loan repayment system, weighing and correlating all the pros and cons that are relevant for a particular situation.

On the one hand, the total overpayment on the loan under the annuity system of debt repayment turns out to be greater than under the differentiated scheme. But, on the other hand, with a differentiated system, the primary credit load (the first few months of using a loan) is significantly higher than with an annuity.