The interest calculation is always interesting in financial mathematics when it comes to investing money or taking out a loan. Investments are of course about the greatest profit that can be made from an investment. When it comes to loans, the aim is to achieve the lowest possible interest rate. However, other factors also play an important role when calculating the interest rate, especially when calculating the effective interest rate.
Calculate annual interest
In order to calculate how much profit can be expected with a certain investment, the following interest formula is usually used:
Z = K * p%
Z stands for the accruing interest, K is the capital used and p% is the interest rate for the capital investment. The formula is pretty simple. Inserting the variables makes it easy to calculate the interest. The capital is known and the bank states the interest rate. An example calculation can be based on the following figures: K = 1,000 euros, p% = 3, which results in p = 0.03.
Z = 1,000 * 0.03
Z = 30 euros
In one year there will be 30 euros in interest on the 1,000 euros invested.
It is different with a loan
It looks a little different with a loan. In addition to the interest, there are additional costs that together make up the effective interest rate. The main part of this is due to the nominal or debit interest. This is a percentage that expresses how high the interest on a loan is as a percentage of the loan amount. The nominal interest rate is usually fixed and remains the same over the entire term of the loan. Variable nominal interest rates change every few months. In addition to this interest, there are additional fees, which determine the effective interest rate (see bpb.de). These include, for example, fees for account management, commissions or commitment interest. If you compare several loans, you can use the effective interest rate as a guide to find the cheapest offer. Anyone who knows the interest rate can use the Credit calculator from creditmaxx.de calculate exactly how much interest is actually to be paid over the entire term.
Calculate interest rates, time periods and principal
The individual equations in financial mathematics can be simply rearranged so that each value of the formula can be calculated, for example how high the interest rate is if the capital and interest rate are known. If necessary, you can also calculate exactly how long it will take for a certain amount of interest to be worked out with the investment.
To calculate the interest rate, the following formula applies:
p% = Z / K
The capital is calculated from:
K = Z / p%
The period is calculated from:
m (months) = (Z * 12) / (K * p%)
t (day) = (Z * 360) / (K * p%)
Calculate compound interest
Interest calculation is the easy part of finance. It gets more complex when it comes to calculating compound interest. In many cases, an investment is a long-term affair, usually ten or 20 years. In order to calculate the interest here, it would be very time-consuming to always calculate with the annual interest rate formula and to recalculate the rate formula for each year. The result of the previous year plus the capital would always be the basis for the calculation for the next year. Investors also do not want to know how much money they will make in a period of one year. What matters to you is how much money is in the account at the end of the planned period. The formula for this is as follows:
Ka = K * (1 + p%)a
In this formula, K isa the capital that is in the account after a years. K stands for the capital at the beginning and p% is again the interest rate. a stands for the term in years.
Borrowing costs – other factors are relevant
Those who apply for a loan know in advance that there will be costs involved. The amount of the loan costs depends on various factors. For example, if you apply for a loan of 10,000 euros and pay a nominal interest of 5%, you have to pay 500 euros. If there is an account management fee of 100 euros, the effective interest rate is 6%.
Can the nominal interest rate change?
If the nominal interest rate at a financial institution is high, the loan becomes significantly more expensive. Higher nominal interest rates raise loan rates. The following values ​​can influence the interest rate:
- ECB key rate according to bundesministerium.de
- Term of the loan
- Amount of credit
- Creditworthiness
- Usage
The key rate is specified. It shows how much money the bank pays to receive money from the ECB. If the key interest rate rises, the banks’ nominal interest rates for the various financial products increase automatically. When key interest rates rise, it is more advantageous for financial institutions to use the customers’ funds. However, if the key interest rate falls, it is cheaper for the bank to borrow money from the ECB. Ultimately, the borrowers benefit from this.
What influences the individual loan offer?
Term and loan amount are two essential factors that influence the individual loan offer. Financial institutions charge higher interest rates the longer it takes for the loan to be repaid. This increases the cost of credit. This also applies to the loan amount. The more money a borrower borrows, the more expensive it will end up being. With a good credit rating, customers benefit from a lower interest rate. Because the bank then assumes that the customer pays his loan in full and on time. For the bank, the risk of default falls if the customer has a good credit rating.
If the loan is linked to a specific purpose, there are usually also cheaper interest rates. If the loan is intended for the purchase of a vehicle or real estate, these are additional security for the bank. This reduces the nominal interest rate and thus the loan costs.
Rule of thumb for the loan costs:
Borrowing cost = (loan amount * effective rate) / 100
A loan of 10,000 euros with an effective interest rate of three percent results in loan costs of 300 euros.