When a loan is drawn on, the borrower also incurs some additional costs. In order to be able to compare different offers with one another, but also to know which charges are to be expected or how long the loan has to be repaid, it makes sense to be able to calculate a loan.

In contrast to a mortgage loan, where you also have to take account of the repayment, it is relatively easy to calculate an installment loan. There are a few tools available online with the online loan calculator. However, it is also not difficult to do the calculation yourself. In most cases, one would like to calculate the amount of the monthly loan installment. If you already specify the rate, you can of course also calculate the other components.

The interest calculation with the commercial interest formula is useful for easy calculation of a loan. The interest calculation is regarded as an applied form of percentage calculation.

## Interest calculation:

In order to calculate the interest (nominal interest), the following key figures must be given:

Capital (K), interest rate (p) and time (t). As an explanation, it should be stated that under capital the

Loan amount must be understood.

Example: financing a car purchase

K = 20,000 USD; Nominal interest rate 6%, t = 3 years, processing fee 2%

First add the processing fee of 2% of $ 20,000 = $ 400 to the loan amount. Added to this are the total interest (6% per year over 3 years), which corresponds to an amount of $ 1,200 per year equal to $ 3,600. The total amount of $ 24,000 is now divided by the term of 36 months and the monthly credit installment is $ 666.67.

In most cases, the banks modify the interest rates so that the interest payments correspond to the term and the credit rating. Short-term loans usually earn interest on a daily basis and have higher interest rates than longer-term loans, which are subject to lower interest rates. The creditworthiness of the borrower is also decisive for the amount of the interest rate. The interest rate reflects the risk the bank is taking. If the credit rating is poor, the risk for the bank is high. The interest rate required by the bank will rise accordingly.

In the repayment calculation (usually a long-term loan), the loan is repaid in several installments at the same time intervals. A distinction is made between the repayment loan and the annuity repayment. With installment repayment, the repayment rate remains constant during the term and does not change. With annuity repayment, it is the annuity that remains constant. The annuity consists of the repayment and the interest rate. The repayments lead to a decrease in the remaining debt. The falling residual debt leads to falling interest obligations. The more the interest obligations decrease, the more the repayment portion in the annuity increases.

## Procedure for repayment in installments:

The debt of $ 30,000 is to be repaid in 5 years. The subsequent interest rate is 7.5% and the repayment rate is $ 6,000 per year. The first and fifth years are shown here as examples.

1st year: remaining debt 30,000; Interest payment 2,250; Repayment rate 6,000; Annuity 8,250;

5th year: residual debt 6,000; Interest payment 450; Repayment 6,000; Annuity 6,450;

The sum of the annuity is made up of the amounts of the interest payment and the repayment rate.

Annuity repayment procedure: Source: “http://www.it-infothek.de/fhtw/semester_2/bwl_2_09.html“

With annuity loans, the borrower pays the same annual amounts (annuities). This is achieved by increasing the repayment portions over time, since the interest portions decrease over time due to a reduction in the remaining debt. The annuity is determined by multiplying the present value of the loan by the capital recovery factor. After calculating the respective annual interest, the remaining amount remains for the repayment.

Example: A loan of $ 100,000 is granted at an interest rate of 10% over 5 years.

annuity:

100,000 × 0.263797 = $ 26,379.70

## Repayment of an annuity loan

Here, too, the development of the annuity loan using the example of the first and fifth years.

1st year: remaining debt 100,000; Interest 10,000; repayment 16,379.70; Annuity 26,379.70; Remaining debt 83,620.30;

5th year: remaining debt 23,981; Interest 2,398.18; Redemption 23,981.52; Annuity 26,379.70; Debt 0.29

Annuity loans are often given as private loans by banks because the constant rate offers the customer a good basis for calculation. Annuity loans are a type of real estate finance. In Germany, the interest rate is fixed for five, ten or 15 years.

- Either the contract can be terminated afterwards or a new interest rate has to be negotiated to continue.
- Another option is to agree on a variable interest rate that is updated regularly depending on Cream Bank or a related index. It is also possible to replace the annuities with fixed monthly installments, in which case one twelfth of the nominal annual interest rate is then payable. This is the most common form in Spain. Here, however, the customer bears a much higher risk, which is why a much lower interest rate is required.
- Furthermore, a distinction is also made between a maturity loan. Here the loan debt is repaid at the end of the term. It can be the end of a fixed agreed term or after a termination. During the term, the burden is limited to the payment of interest. Here, too, an example from the first and fifth years of the loan.

1st year: remaining debt 100,000; Interest rate 5,000; Repayment 0; Annuity 5,000;

5th year: remaining debt 100,000; Interest rate 5,000; Repayment 100,000; Annuity 5,000;