When a lender lends money to a borrower, the lender charges interest. This is effectively the purchase price for the act of lending. The amount of interest is not agreed as a fixed sum but is calculated as a percentage of the amount of money borrowed. This interest rate on loans is called the nominal interest rate. For comparing loans, the nominal rate alone is not sufficient; the effective interest rate is the relevant figure.
Interest rate – Introduction
People who take out a loan receive a certain sum of money from a bank or a private creditor at a set loan interest rate. They must either repay this over a longer period in small instalments that include the cost of the loan interest rate, or they must settle the full amount of the loan after a fixed agreed time. In the following guide we explain the difference between nominal interest and the effective annual interest rate and provide examples for interest calculation.
What is the loan interest rate?
A loan can be very helpful in many situations. Especially when buying or building a house, most people rely on a loan, but loans can also be necessary for other larger purchases. Buying a new car, a costly renovation at your home, or another large expense can also make a loan necessary.
In many cases, loans are also helpful for smaller purchases, because the required items are immediately available and the customer does not have to save for a long time to buy them. A loan is often very helpful, but it always has its cost.
For providing the loan amount, banks charge a loan interest rate. This means that the customer not only has to repay the loan but will always incur slightly higher amounts to pay the bank for its services. The loan interest rate can be stated in different ways.
We use a loan to purchase or finance something valuable, and the lender charges an interest percentage for that service. The nominal interest and the effective rate are two key measures for understanding how expensive a loan will be for the borrower.
Types of interest
While the interest rate is given in percent, the interest amount refers to the actual monetary value charged as the lending fee for a loan. The interest rate can also be influenced by compound interest.
The term compound interest in practice refers to the interest on interest—that is, previously accrued interest that is added to the principal and itself accrues interest. In mathematics, a big difference is made between linear interest calculation and exponential calculation. The contract must clearly state which calculation method applies.
Another component of the interest rate can be the interest structure, which depends on the duration of the granted loan. When financial advisors speak of the nominal rate, they mean the numerically stated interest rate that is due for a desired loan amount.
If the advisor speaks of the real interest rate, they mean the interest rate after deducting the current inflation rate. Therefore, the real interest rate can sometimes even be negative—if the inflation rate exceeds the nominal rate.
When the term effective interest rate is used, it refers to the rate that results when the nominal rate is related to other price-determining factors.
The phenomenon of a nominally negative interest rate is rare and becomes possible only in times such as a financial crisis.
The money market rate is another form of interest rate. It is used to name the interest rate for cash borrowing on the national or international money market. This money market rate is especially important for transactions between individual credit institutions. The money market rate between credit institutions and the central bank is called the key interest rate. The interest rate for the capital market, which is important for longer-term loans in book money, is also referred to as the capital market rate.
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Deriving the effective interest rate from the nominal rate
The nominal rate is the pure debt interest. With it, a fixed sum for the loan costs can be calculated. A simple example for interest calculation can illustrate the relationship between the different interest components:
With a loan amount of 6,000 euros, 5% interest and a term of 60 months, the interest amounts to 1,500 euros. However, not all loan-related costs are covered by that. Ancillary costs of a loan consist of commissions and processing fees.
Assuming ancillary costs of a total of 500 euros, the loan costs of the example loan rise from 1,500 euros to 2,000 euros. If you convert these costs back into an interest rate, you get 6.67% instead of the original 5%. In this calculation all effectively incurred loan costs were recorded. That is why this rate is also called the effective interest rate, because not only the pure interest calculation is considered, but also commissions and fees are included.
When comparing different loans, only the effective interest rate is suitable as a comparison criterion. The legislator has made the indication of the effective interest rate mandatory.
Nominal rate level depends on several factors
There are various criteria that influence the level of the loan interest rate. The key rate of the European Central Bank is only one factor. It determines the rate at which the bank can obtain funding itself. The bank does not lend its own money but borrows it there.
The bank adds its profit margin to this rate. It also estimates the development of inflation. During the loan term, the amount loses purchasing power.
The bank factors this loss of value caused by inflation into the interest rate as well. It wants to receive back enough money so that the purchasing power of the sum after repayment is at least as high as it was at the start of the loan.
Another surcharge is charged for the expected risk on the interest. The bank's risk lies in a non-repayment of the loan. To assess this risk, the bank checks the borrower’s creditworthiness, the so-called credit rating. The worse this is assessed, the higher the bank will set the risk surcharge.
The last factor is the collateral for the loan. If a tangible asset of lasting value is used as security, for example a property, the interest rate will be moderate. If the loan is intended for a consumer good or pure consumption and the only security is proof of monthly income, the interest will be correspondingly higher.
The nominal loan interest rate
Calculating a loan interest rate (interest calculation) is common in financial transactions. For example, if a customer deposits money at a bank, they receive interest for it. This is added to the initial capital. If, on the other hand, you borrow money from banks in the form of a loan, you have to pay interest for it.
If you receive interest on a savings balance, this is shown as credit interest. If you have to pay interest for a loan, these are called debit interest. The amount of interest or the rate of interest is determined by the amount on which the interest is charged and by the agreed interest rate. Below we provide an example of an interest calculation.
Interest calculation: Example for the nominal loan rate
The interest rate, or interest factor, is expressed in percent and represents the monetary claim demanded on borrowed capital. In financial literature the interest rate is denoted either by the letter i or p. However, the internationally more common term i seems to prevail. For a time, experts also distinguish between the term interest factor, denoted by the letter p, and the interest rate, denoted by the letter i.
If a distinction is made between the interest factor and the interest rate, the interest factor refers to the nominal value before the percent sign.
At an interest rate of 5% the interest factor would be p = 5. The interest rate i = p/100, for example i = 5% = 5/100 = 0.05, while the interest factor p = 100i, which means p = 100 x 5% = 100 x 0.05 = 5.
Interest is usually calculated once a year (simple interest calculation). Here is an example. If you take out a loan of 10,000 euros at an interest rate of 5 percent, this results in 500 euros after one year. However, most loans require monthly instalments. In that case the loan interest is recalculated for each period.
For example, if you repay 100 euros every month, after one month interest is calculated only on a loan amount of 9,900 euros, after another month only on 9,800 euros. To enable this calculation (interest calculation), it is necessary to determine the loan interest rate for each individual day (daily interest).
This ensures that you only ever pay interest on the amount that is actually outstanding at the respective time. Nominal loan interest rates can differ significantly between different offers. Therefore it is always important to compare the loan rates of various offers carefully.
Usage conventions in interest calculation
In finance the banking year is referred to as the "usance". To correctly apply the interest formula, the usance must be clarified. The German method is called 30/360, where the year is reduced to 360 days and each month always has 30 days.
The euro method is referred to as act/360. Here the French usance is 360 days, but the actual days of the months are counted. The English method is called act/365, where the English usance has 365 days and the actual days of the month apply. There is also the act/act method. Here both the current year and the month are based on the actual number of days, which means that in a leap year a 29th of February is counted. On the European money market the act/360 is generally used and the first day of borrowing is not included in the interest rate calculation.
What is the effective annual interest rate?
With a loan, not only interest is charged; there are also many other fees. Many banks, for example, charge a processing fee and a loan fee. Interest-free years can also influence the actual price that the customer pays for the loan. In addition, there are different methods of calculating repayment, which also affect the final total of payments. These additional costs mean that the nominal interest rate is only one of several factors responsible for the size of the monthly instalments.
Therefore, consumers often find it difficult to compare different loans. The actual burden of one loan can thus be higher than that of another loan, even though the nominal interest rate is actually lower. Therefore there is a law in Germany that obliges banks to state not only the nominal rate and various processing fees in a loan agreement, but also the effective loan interest rate.
This indicates how high the total costs for the loan are and includes both interest and all other fees.
Presentation and calculation of the effective annual interest rate
The legislator has also specified a procedure according to which the effective annual rate must be calculated. This standardized procedure (or standardized formula; interest calculation) is intended to guarantee that the effective annual rate is calculated in the same way by all banks and actually reflects the total costs of the loan. For this reason it is always more important for consumers to compare the effective annual interest rate. If the customer only compares the nominal rate, the costs for the loan can still differ significantly.
For a loan agreement, the effective annual interest rate (stated in percent) is mandatory (actual loan costs per year). If the data in a loan agreement were calculated incorrectly and the values resulting from fees and the nominal loan rate should be higher than the stated effective annual rate, the bank is always obliged to reduce the nominal loan rates so far that the agreed effective annual rate is maintained.
Conclusion: Compare loan interest rates quickly and easily
If you need a loan and want to compare the different offers, it is always sensible to pay attention primarily to the effective annual interest rate (stated in percent). This allows you to judge the total costs of the loan at a glance. That way you can estimate how to manage your capital.
If you are looking for an affordable loan, it is advisable to use an online loan calculator. It will show both the nominal rate and the effective annual rate. To keep total costs low, it is always sensible to choose the offer with the lower effective annual rate. An example of the calculation (formula, interest calculation) of the interest rate can be found above.
Glossary: important terms on interest rates
Compound interest: In finance, this denotes interest due that is added (capitalized) to the capital (initial capital) and in the future is remunerated together with the capital at the applicable interest rate.
Loan interest: Loan interest refers to the interest charged that must be paid for a loan. Interest is levied as a fixed percentage of the loan amount. Therefore the rule of thumb applies: the higher the loan amount, the higher the interest amounts. A distinction is made between the loan rate, the debit interest rate and the effective annual rate. The latter includes, in addition to the loan interest, the incurred costs—i.e. fees and commissions for the loan.
Daily interest: If interest must be calculated for a period shorter than a year, this is referred to as daily interest. Daily interest and overnight deposit interest (Tagesgeldzinsen) are often confused. However, overnight deposit interest refers to an overnight deposit account and is calculated annually. Daily interest, on the other hand, refers truly to a single day.