Compound Interest Equation

Before examining the subject of the combined interest equation, it is necessary to make a brief explanation about the interest. Then we will continue with the unified interest equation.

Compound Interest Equation

Information About Interest

When you want to take a loan or cash advance from a bank, you will borrow for a certain interest. It will apply different rates of interest depending on the maturity and amount you want. As a result, you will have repaid more money than the first one. This is the simplest expression of the subject of interest. You pay a certain interest not only for banks, but also for a product you buy as we call an open account.

Let’s take a look at information about interest and calculation methods:
What is Interest?

The money received against the operation of the money given as a loan from a bank or a similar place is called interest. Interest rate varies depending on certain issues. The primary issue is maturity and principal amount. For example; banks lend money at a more favorable interest rate until a certain amount and maturity.

To define the interest in terms of economy; It is the income obtained as a result of the sales resulting from the debt agreement. According to capitalism, interest corresponds to the income from capital used as input for production purposes. The reason for this is that capital, which is among the factors of production, is used in a certain period and in return, it is repaid at interest rate.

compound interest equation
compound interest equation

Simple and compound interest calculation for both borrower and lender; it is extremely important because you can make return-to-debt comparisons correctly. Therefore, interest is also interpreted as the basis of financial mathematics.
What is Simple Interest?

Since simple interest is only interest calculated on principal, we can say that there is a straight logic calculation method. If we immediately formulate;

Interest Amount = Principal * Interest Rate (%) * Maturity

One of the issues to be considered in this type of calculation is that the interest rate is the subject of operation as a percentage. In other words, when 6 percent interest rate is said, the relevant account is made as 0.06.

Another issue to be considered in the calculation is maturity. You should know that a calculation is made on a yearly basis. In other words, when 6 months maturity is said, calculation is made over 0.5 from 6/12 equation. If for 90 days, you should trade approximately 0.25 from 90/365 equation.

What is Compound Interest?

The type of interest in which the sum of the principal and interest obtained in a unit period is accounted as the principal in the subsequent unit periods and is calculated over this new amount is called a compound. In other words, the amount of principal increases for each period compared to interest. In the next period, interest is calculated again on this amount. At this point, a concept called interest rate is included in the equation.
How Compound Interest is Calculated?

Although the logic of compound interest calculation is also easy, performing separate calculations for each period can cause confusion. Therefore, it is useful to go step by step.

To give an example for compound interest; While the compound return of 2000 Turkish lira with a 3-year maturity of 10 percent interest rate is calculated, 2200 liras, which the principal will reach with its interest at the end of the first year, is the principal invested in interest in the second year. This time, the transaction will be made over 2200 lira and at the end of the second year, 2420 lira will be principal. In the third year, calculations will be made over 2420 liras and at the end of the third year, the principal will be 2662 Turkish liras.

When we formulate this process;

Amount Reached at the End of the Period = Principal * (1 + Term Interest) Recurring Period

It is possible to revise this formula for annual, monthly and quarterly periods. Namely;

Annual = Principal * (1 + Term Interest)

Quarterly Periods = Principal * [1 + (Term Interest / 4)] 4

Monthly Periods = Principal * [1 + (Term Interest / 12)] 12

While calculating with the formula, your head is likely to get confused again. You can simply calculate compound interest on the interest calculator above.

Negative Interest Rate

compound interest equation

High Interest Savings Account

High Interest Savings Account; You can evaluate your savings with time deposits offered by banks. When you promise not to touch your money during the maturity you set, your money in the bank will increase by the determined interest rate.

You can use our deposit calculation tool to see the term account interest rates and make calculations. You can learn the interest rates by using the calculation tool and see how much deposit interest yield you can get from which bank.

High Interest Savings Account

In the most suitable deposit gain calculation form, you can enter the amount you want to use for the deposit account, the duration of your deposit (in days, months, years) and click on the find the most suitable button to go to the listing page. You can access the details of the deposit accounts you want from the list and apply for the most profitable one for you. In the detail pages, you can also review a table listing interest rates based on the duration of the term on a day basis and change your maturity preference if you wish. If you want to apply, you will go to the screen where you will fill out the form required to open your account without any further action. When you submit the form by entering the personal information requested by the banks in the form here, your application process is completed. It proposes you to have an orange account deposit with the most favorable advantageous interest rates.

high interest savings account
high interest savings account

Even if you withdraw money whenever you want, you can win with the e-Term Account, which does not deteriorate!

e-Term Account is a time deposit account that you can open easily from Banks Internet or Banks Mobile. Open an e-Term Account from Banks Internet or Banks Mobile immediately, and benefit from the campaign that suits you.

Welcome Campaign: If you have not opened a term account in the last 1 month and you do not have a current account, you can use the campaign by opening an e-Term Account between the campaign amount * and maturity intervals.

Long Term Campaign: You can benefit from the campaign by opening an e-Term Account in the amount of the campaign * and maturity intervals.

Your total time deposit, which is taken into account by the bank after the account opening, must be in the campaign amount range. Your campaign account will limit with standard e-Term interest rates.

Advantages of e-Term Account:

Always higher interest in e-Futures: With the e-Futures account that you can open with different terms and amounts, you can always benefit from interests above the sign interest rates for your deposit account.

e-Term earns from the date of opening: Since the maturity start date of e-Term deposit accounts is the same as the account opening date, you start earning interest from the moment the account is opened.

e-Term is a flexible account: When you take a partial withdrawal from your account before the due date, the balance remaining in your account continues to be evaluated with the same maturity and interest rate, only interest amount is not obtained for the amount you withdraw before the due date.

  • You can take advantage of withholding tax in your time deposit accounts opened in the long term.
  • When opening your account, you can instantly decide how your interest rate and principal will be evaluated during the account opening.
  • Currencies You Can Open Account: USD, EUR, GBP, USD, EUR, JPY, CHF, GBP, SEK, SAR, RUB, NOK, DKK, CAD, AUD
  • Account Opening Lower Limits: 1.000 USD, EUR, GBP, 1.000 USD, 1000 Euro, 1000 GBP, 10.000 JPY and 1.000 currencies for other accounts.
  • The interest rate is gross.
  • Special interest rates for Banks Internet Banking and Banks Mobile are valid for all terms including broken terms from 28 days to 365 days.
  • Your time deposit account that you open from Banks Internet Banking and Banks Mobile is limited to these channels with a special interest rate.
  • No interest can be used on accounts that have been disrupted before their due dates.

Expiry Options

While opening the account, you can choose one of the expiry options below.

Principal and Interest Extension: Your account is automatically renewed at the end of maturity with the same maturity and current interest.
Principal Extension: Only your principal is renewed, the interest amount is transferred to the account you choose.
Conditional Extension: The amount you set is transferred to a selected account and the remaining amount is renewed.
Don't deny: Your account is closed by transferring the principal and interest amount to the accounts you choose.

Automatic Deposit to Time Deposits

You can automatically add money to your time deposits with the Term Deposit Order. With the instruction you give from our Branches or Banks Internet Banking, the amount you specify is transferred from your demand deposit account to your time deposit account at each renewal.

Interest Rate Parity

high interest savings account

Calculate Compound Interest

Calculate Compound Interest

Calculate Compound Interest, Simple interest calculation was a method applied in short-term (less than 1 year) loan transactions. In addition, in the simple interest method, the principal is fixed for each period and the interest amount obtained in that period was not added to the principal in the next period.

Calculate Compound Interest

Compound interest calculation, on the other hand, is a method applied in long-term (more than 1 year) credit transactions. In this calculation, capital does not remain constant. In other words, the interest amount calculated at the end of each period is added to the principal deposited at the beginning of that period and the principal for the next period is created. In other words, the fish value of a period is the principal of the next period. Thus, the amount of interest to be obtained in each period is not the same as in simple interest and increases increasingly. Because, interest is applied to the interest amount obtained in each period in the next period.

With the compound interest application, the investment made is guaranteed more than any simple interest against any possible risk.

If the compound interest calculation is done for certain periods (monthly, 2-month, 3-month, 4-month, 6-month, …), if it is calculated as “intermittent compound interest calculation” with very small time intervals, it is also called “continuous”. or instant compound interest calculation ”.

The symbols used in compound interest calculations are the same as in simple interest. The basic formulas are as follows: * Total amount that the principal will reach at the end of the period with the discrete compound interest calculation (fish)

A=a(1+t) n

Total amount to be reached by the principal at the end of the period with the continuous or instantaneous compound interest calculation:

A=a.en.t, e=2,718281…

Since the concept of logarithm in mathematics should be known in some questions to be solved in this section, let us briefly remember the logarithm operation and its important features:

Periodic Interesting

Periodic interest is the process of making interest calculations for a fixed capital (may be 1 year) at more than one equal intervals.

Although it was applied to savings deposits by banks in previous years, it is mostly used in the interest of long-term, low interest loans extended to investors, especially in order to support medium and small sized enterprises. If the term is long and interest is low and the business is considered risky, banks want to receive interest payments periodically for the loan they give. Banks prefer to use the effective interest rate to support the customer and make the payments attractive in the periodic payment of short-term bank loans.

In addition, periodic interest is used by institutions and organizations within the scope of money and capital markets. For example, payments to holders of bonds (= interest debt issued by government and companies) are also periodic.

The periods of interest payments and interest rates are written on the bonds. Interest payments are made at regular intervals. When the bond expires, the principal is also paid to the bond owner. Interest payments of bonds are a good example of periodic interest rate transactions. However, since there are different types of bonds and different payment methods, we will not be concerned with these parts here. We will only mention the part we will use in our class and especially the interest payments made in 3, 4, 6 months in 1 year.

Note 2: For the transactions we will perform in this section, we can give a summary information as follows: In the problems related to the compound interest calculation, if the interest cycle includes less than 1 year or periods and the interest rate is given annually; The t interest rate and the number of n periods should be adjusted to match each other.

Negative Interest Rate

Interest Rate Parity

Interest Rate Parity

Interest Rate Parity… It is possible for international financial capital to move freely on a global scale, thanks to increases in the level of integration of financial markets.

It is a result of this development that the economic decision units, which can be named as global investors in the day-to-day, can perform their transactions quickly and instantly in the event of a profit opportunity that may occur between the markets. This situation increases the importance of financial markets day by day for investors and economic policy makers.

The most important criterion that decision units operating in global markets take into account when making investment decisions is the “risk-return” relationship. As it is known, there is a correct relationship between risk and return. Investors determine their portfolio preferences by comparisons between the possible returns of domestic and foreign assets. In this sense, the fact that the domestic interest rate is higher than the foreign interest rate brings domestic assets to the fore and the opposite situation brings foreign assets to the fore. However, to invest in a foreign currency asset When the decision is made, a possible foreign currency risk may be encountered for the depreciation of the exchange rate in the future.

In general, investors are considered to prefer risk-free assets over those at risk. However, this does not mean that economic decision units always demand a risk premium. There are also examples of decision units that turn to risky assets without waiting for a response and even give privileges to risk-bearing assets. The investor profile is divided into three parts in this sense: Those who avoid taking risks, those who avoid taking risks and are insensitive to risk.

The subject of this study is the interest rate currency and the degree of efficiency of financial markets, which explains the relationship between interest, the return of financial assets, and exchange rates. In the study, firstly, the interest rate parity and its basic versions, the safe and precarious interest parity, will be mentioned. The importance of the risk premium within the scope of the insecure interest parity will be tried to be explained. Secondly, the theory and degrees of market efficiency will be explained. Two basic assumptions required for an efficient market will be emphasized. Thirdly, there will be a literature review regarding the secured-insecure interest parity and effective market hypothesis. Fourth, the data set and methodology required for econometric analysis will be introduced and the results of the application will be explained. Finally, the conclusion and evaluation section where the validity of the interest parity and market efficiency hypothesis will be explained for the countries included in the study will be explained.

Interest Rate Parity Theory

Interest rate parity is an important approach that explains the relationship between the returns of financial assets in different markets (Melvin and Norrbin, 2013: 115). In general terms, it expresses the need for similar securities that are priced in different currencies among international financial markets to have the same return (Krugman and Obstfeld, 2009: 336). It is basically examined in two parts: Secured and insecure interest parity.

Secured Interest Parity

Secured interest parity is the process of selling the foreign currency earnings expected in the future through the forward exchange agreement as of the current period in order not to cause unexpected losses in the exchange rates. Secured interest parity protects investors against losses caused by exchange rate risk, on the other hand, provides a useful way to gain the advantage of interest rate differences.

Futures contracts are an application that investors apply in futures markets. These contracts include forward-looking agreements that clearly show the exchange rate at which foreign currency will be converted into domestic currency at the specified maturity and are not the same as the exchange rates at the time the transactions are executed (spot rate).

According to the secured interest parity, it can be said that an investor who avoids risk has two alternatives for financial market investments.

(i) Investors who evaluate their investments with domestic interest rate will earn (1 + R) income for each domestic currency invested at the end of the maturity determined. (ii) Investors who want to evaluate their investments with foreign interest rate, on the other hand, consider the risk of exchange rate. will be in front of you. One unit of foreign currency (1 / S) per unit of currency The investor will earn (1 + R *) (1 / S) amount of foreign income at the determined maturity date. However, in case of using futures contracts to eliminate the currency uncertainty that will occur due to the uncertainty of the future value of the exchange rate, (1 + R *) (F / S) amount will be obtained at the end of maturity.

Insecure Interest Parity

The insecure interest parity implies that a difference between domestic and international interest rates should be equal to the “expected” change in the future value of the exchange rate. An unexpected change in any of these three variables will bring the spot rate re-arrangement.

Term foreign currency contracts are not used in the insecure interest parity. Basically, the idea of ​​converting the revenues to be obtained from foreign currency-based assets into a local currency by using the “expected exchange rate” at a future date is included. However, not knowing the expected spot rate in the future may put investors at risk of exchange rate.

Investors will be risk neutral (risk neutral) if they do not have complete information about future ways of exchange rates. This means that capital owners are only concerned with the expected return of their investments, but not with risk.

As with the secured interest parity, it can be said that investors have two alternatives for the financial market investments in the insecure interest parity (Copeland, 2005: 85-86):

(i) Investors who evaluate their investments with the domestic interest rate, (1 + R) will be generated for the unit.

(ii) Investors who want to evaluate their investments with a foreign interest rate, on the other hand, (1 / S) unit exchange in exchange of one unit of domestic currency and at the end of the determined maturity (1 + R *) (1 / S). ) they will earn some foreign income. When it converts its foreign currency revenues into the national currency at the end of the term, it will move from the exchange rate in the current period and will obtain (1 + R *) (SE / S) amount of domestic currency with the expected exchange rate planned before the investment.

Interest Rate Parity

Fed Interest Rate

Fed Interest Rate

Fed Interest Rate… The Federal Reserve (Fed) pulled the policy interest rate to the range of 0-0.25 percent and launched a $ 700 billion monetary expansion.

The US Federal Reserve (Fed) cut interest rates for the second time before the Open Market Committee (FOMC) meeting on 17-18 March to alleviate the economic impact of the new type of coronavirus (Kovid-19) outbreak.

Fed Interest Rate

In a statement from the Fed, it was pointed out that the Kovid-19 epidemic harmed society in many countries, including the United States, caused disruptions in economic activities and significantly affected global financial conditions.

The current economic data indicates that the US economy has entered this challenging period strongly, and the data from the FOMC meeting since January showed that the labor market remained strong until February and that economic activities increased at a moderate rate.

Interest decision from the Federal Reserve (Fed)

In the statement, it was stated that the energy sector has been under stress recently, and annual inflation in general and food and non-energy items remained below 2 percent, while long-term inflation expectations showed little change.

In the statement, which emphasized that the effects of the Kovid-19 outbreak will focus on economic activities in the near future and that a risk will be created for the economic outlook, it was stated that, in light of these developments, the committee decided to reduce the policy rate of the FOMC to the range of 0-0.25 percent.

The statement said that the interest rate cut will help support economic activity, strong labor market conditions and the committee’s return to the 2 percent inflation target.

It was emphasized that the committee will continue to monitor developments that will affect the economic outlook, including public health, global developments and silent inflation pressures, and will use appropriate tools to support the economy, and use all of the tools to support the Fed’s credit flow to households and businesses and price stability targets with maximum employment. It was stated to be ready.

In the statement, it was noted that the committee will increase the value of treasury bonds by at least $ 500 billion and mortgage-backed bonds by at least $ 200 billion in the coming months to support the smooth functioning of markets for treasury bonds and mortgage-backed bonds, which are at the heart of the household and business loan flow. Thus, a total of $ 700 billion in monetary expansion was initiated.

It was reminded that overnight and forward repo transactions were also expanded, and it was underlined that the committee will continue to closely monitor market conditions.

With the growing concern about the economic effects of the Kovid-19 outbreak, the Fed lowered its policy interest rate by 50 basis points to the range of 1-1.25 percent on 3 March.

After the Fed cut interest rates to zero, the euro / dollar parity increased by 1 percent to 1.12, while the dollar / lira parity dropped below 6.30.

US President Donald Trump congratulated the Fed on the interest rate cut decision and expressed that he was very happy.

Fed Interest Rate