Formula of compound interest for a loan. Compound interest: formula
Most loans today are repaid using annuity payments, the same monthly amounts. Similarly, a steady interest charge is made on deposits. The same amount every month. In banking practice, such interest is called simple. Thus, in the case of a loan every month, its owner will have to repay not only a part of the principal amount, but also a calculated percentage for its use. This partnership format is legal. It is quite another thing if a complex percentage is removed from the borrower. The formula for its calculation will be discussed below.
Against the law, or How do banks profit from inexperienced borrowers?
Many will be interested to know, but charging a compound interest on a loan is illegal. This format of cooperation makes the banking product very profitable for financial institutions and completely unprofitable for the client.Illegal interest accrual is carried out when the interest rate throughout the entire loan period is systematically changed. It is possible to notice illegal actions of a bank only when a delay is formed, which in fact should not be. In the course of legal proceedings, it is possible to prove that the bank has charged an incorrect percentage.
So what is it - compound interest on the loan and deposit?
The compound interest formula for a loan will make it possible to understand that the charge is made not only on the principal amount of the debt, but also on the amount of funds that was formed after the accrual of bank interest. Simply put, compound interest is interest that accrues on itself. In banking practice, they are also called double interest.
People often face situations when their small debt turns into a tidy amount of funds. The essence of the problem is that after a financial institution records a delay, it will add a percentage to the amount of the debt. The next accrual will be made on the principal amount of the debt plus the percentage calculated on it earlier. Debt to the bank increases exponentially.Unprofitable compound interest for the borrower becomes a real advantage for investors, since, similarly to the increase in debt, they provide a quick profit increase.
Compound interest: formula for borrowers
In financial practice is very common scheme for calculating compound interest. It is relevant if interest funds are not paid every month, but are added to the size of the principal debt, which becomes the new base for bank charges. If the loan has a duration of a year or more, the borrower may face its insolvency.
It helps to calculate the compound percentage formula below. It is focused on the analysis of only one accrual period.
FV = PV +% = PV + PV *% = PV * (1 +%)
To calculate the overpayment for the two accrual periods, you can use the following formula:
FV = (PV +%) * (% + 1) = PV * (1 +%) * (1 +%) = PV * (1 +%)2
Calculate the amount of overpayment for any other number of periods will help formula for calculating compound interest:
FV = PV * (1 +%)N= PV * Kn, where:
- FV - the accrued amount of debt.
- PV is the primary amount of debt.
- % - rate for the accrual period.
- N is the number of charging periods.
- KN - the rate of accumulation of compound interest.
Building up simple and compound interest
Formulas of simple and compound interest allow you to determine the amount of overpayment and pre-evaluate the benefits of the banking product. With short-term loans, simple interest turns out to be more profitable for banks. However, if the loan term has medium or long-term trends, the difference can be very noticeable for the client. From here come the following patterns:
Regardless of the interest rate at:
- 0 <N <1, then (1 + N *%)> (1 +%)N.
- N> 1, then (1 + N *%) <(1 +%)N.
- N = 1, then (1 + N *%) = (1 +%)N.
As you can see, financial institutions issuing loans, get more benefits from simple interest when calculating the entire income once to the end of the entire loan period. Compound interest brings benefits only if lending is carried out for at least a year. Both types of interest give identical profit to the bank if the loan is issued for a period of one year, and interest is calculated once at the end of the partnership.
Formula for compound interest on deposits
Compound interest is used by banks not only to obtain the benefits of lending. The accrual format is also applied when making deposits, thereby determining benefits for investors. The total amount of the contribution can be calculated using the following formula:
S = D * (1 +% * i / Y / 100) * N
To calculate the profit on the deposit it is effective to use other formulas:
Sp = S - D = D * (1 +% * i / Y / 100) * N - D
Sp = D * ((1 +% * i / Y / 100) * N - 1)
To compare the profitability of deposits that are decorated for a different period and for each of which has its own compound interest rate, the formula will look different. It will allow you to determine the percentage that an investor will receive after capitalization.
P1 = 100 * ((1 +% * i / Y / 100) * N - 1), where:
- D - the size of the primary contribution.
- S - the total amount of the deposit with accrued interest.
- % - interest rate.
- Sp - income.
- N - the number of charges.
- i - the number of days on interest accrual.
- Y - days in a year.
The total bank rate calculated with the capitalization of interest is called effective. Financial institutions do not take into account the day the partnership ends, if they use a complex profit accrual scheme.
An example of the calculation of complex charges on the contribution
The formula for calculating compound interest helps each investor to estimate in advance the amount of his income. Let us try to calculate the total amount of the deposit and the profit separately obtained from it, if the size of the initial investment was 100,000 rubles for a period of 90 days at a rate of 16%.
S = 100,000 + (100,000 * 16% * 90/365)
S = 103945.2
Sp = 100,000 * 16% * 90/365
Sp = 3945.2
What to pay attention to?
For each format of partnership with the bank you need to use an individual version of the calculation. Depending on the duration of the deposit and the frequency of payments, the final compound interest will be formed. The formula for its calculation will vary from case to case. In order to avoid mistakes and choose the most profitable deposit program, you need to contact the experts. Help in this matter can representatives of the financial institution. Although they are not entitled to recommend deposits, they are obliged to provide, upon request, a complete scheme for calculating interest on them.
Capitalization when investing in foreign exchange markets
Interest capitalization is found not only in the bank, but also in the Forex market. Investors who give their capital in trust, are able to follow the increase in their deposits exponentially. The specificity of this type of investment is that when profit is received, it is not immediately removed, but is distributed at the end of the trading period. During the trading period, which can be a week, a month, or even several months, the compound interest will be automatically accrued due to the nature of the trade.The formula for compound interest on deposits will not be suitable for accurate calculation of income. The reason is the lack of a stable rate. Profit is determined by the quality of the trade manager, his strategy and money management policy, other parameters of the trading system.
To calculate the income during capitalization, not one compound interest formula for a loan and a deposit is used, but several. This is due to the different terms of partnership with the bank. Interest on interest can be carried out every day, which is very rare, every week, every month and even every year (with long-term investments).
The best option can be considered a deposit with a monthly capitalization, it is easy to find it, and it will bring benefits rather large. The accrual of interest on interest is the more profitable for the investor, the more often the charge is made. Despite lower interest rates on bank products with capitalization, the profit ultimately turns out to be an order of magnitude greater than with a simple accrual scheme.
Another interesting point is that the longer the deposit is in the bank, the faster it will grow.The increase in income will be due to the addition of accruals to the basic amount of funds. If during the year the advantages of capitalization are not so tangible, after ten years of doubt, the advantages of this banking offer will disappear. Thus, choosing a lower interest rate, but dwelling on capitalization, you can get a higher profit on the deposit.