To solve this, we'll break down the problem into manageable steps for each part.

a) What will be the amount of your monthly repayment after the agreement with the bank?

First, let's figure out what the outstanding loan balance is after 3 years, before the special repayment of €2,000.

Step 1: Calculate the outstanding loan balance after 3 years

We will use the amortization formula to find the remaining loan balance.

The formula for the loan balance after $t$ months is:

$A = P \times \left( 1 + \frac{r}{12} \right)^t - \frac{M \times \left[ \left( 1 + \frac{r}{12} \right)^t - 1 \right]}{\frac{r}{12}}$

Where:

• $P$ is the principal loan amount (€12,000),
• $r$ is the annual interest rate (4.2% = 0.042),
• $t$ is the number of months (3 years = 36 months),
• $M$ is the monthly payment (€250).

Substituting the values:

[ A = 12,000 \times \left( 1 + \frac{0