The process of modelling usually includes the translation of a real world problem to a[br]mathematical problem. We start the modelling cycle by giving assumptions:[br][list][*]We are credit-worthy for all appearing credits.[br][/*][*]There exist only four credits and one key interest rate p (think of Euribor):[/*][*][table][tr][td][b]Credit 1:[/b] The credit interest rate p[sub]1[/sub] equals the key interest rate p in every[br]interest rate period.[/td][/tr][tr][td][b]Credit 2:[/b] The credit interest rate p[sub]2[/sub] is 1% in the rst period, 2% in the[br]second period and in the following periods p[sub]2[/sub] equals p.[/td][/tr][tr][td][b][/b][b]Credit 3:[/b] The credit interest rate p[sub]3[/sub] takes only values in a certain interval[br][2; 7]. If the key interest rate is below 2, then p[sub]3[/sub] equals 2 and if the key interest[br]rate is above 7, then p[sub]3[/sub] equals 7, otherwise p[sub]3[/sub] equals p.[/td][/tr][tr][td][b][/b][b]Credit 4:[/b] This credit is a foreign currency loan, particularly in Swiss franc.[br]We assume that this credit depends on the key interest rate p as well. In[br]the real world this is not the case, because one takes his debt in Swiss franc,[br]so the credit interest rate has to depend on the Swiss-Libor. As expected,[br]the exchange rate is important on such forms of credits. We denote er as the[br]exchange rate which says how many Swiss franc we get for one Euro. We don't[br]distinguish between bid and ask price and assume er to be constant over the[br]lent term.[/td][/tr][/table][br][/*][*]For convenience the interest rate period is one year.[br][/*][*]The key interest rate is variable, but constant over the whole credit term.[br][/*][*]The value of the instalments, the annuities, is constant over the whole credit term[br]and accounts for 8 400 Euro. One pays such amounts in arrears. In other words,[br]at first the debt level will be raised by interest rate and then it will be reduced by[br]paying the annuity amount.[br][/*][*]We neglect all kind of charges and taxes related to the borrowing.[br][/*][/list][justify][math][/math][/justify][justify]Now, we shortly introduce the most important mathematical tool for this article the[br]"repayment-equation" and assume that the reader knows the following equation very[br]well. We identify important variables and denote S for the start level of debt, S[sub]n[/sub] for[br]the debt level after n years, R for the yearly instalments and p for the value of the key[br]interest rate in percent. The recurrence relation for S[sub]n[/sub] is:[br][math]S_n=S_{n-1}\cdot\left(1+\frac{p}{100}\right)-R[/math][br][br]One finds an explicit version below:[br][math][br][/math][math]S_n=S\cdot\left(1+\frac{p}{100}\right)^n-R\cdot\frac{\left(1+\frac{p}{100}\right)^n-1}{\frac{p}{100}}[/math][/justify]Which criteria are needed to mark the best credit? One assumption assures the constancy[br]of the instalments over the whole credit term. Then it's almost obvious, the best credit is[br]the one with the shortest lent term. In the following we are going to simulate the process[br]of the four different credits. An interest rate of a credit depends on the key interest rate[br]p, so the value of p represents the essential feature and is the one to be modelled. The[br]modelling takes place in a GeoGebra applet. We start with deterministic and end up[br]with probabilistic considerations.