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The question involves calculating the monthly payment for a linear loan where a company finances a new depot with a 30-year mortgage of €360,000 at an annual nominal interest rate of 6%.

**Solution Steps:**
1. **Total loan amount:** €360,000
2. **Loan term:** 30 years (or 360 months)
3. **Annual interest rate:** 6%
4. **Monthly interest rate:** \( \frac{6\%}{12} = 0.5\% \) per month

A linear loan implies that the principal repayment portion is constant every month. Therefore, the principal to be repaid each month is:
\[ \text{Monthly Principal Repayment} = \frac{\text{Total Loan}}{\text{Loan Term in Months}} = \frac{360,000}{360} = 1000 \, \text{euros} \]

The interest payment decreases each month as the remaining principal reduces. The interest for any month \( k \) is calculated as:
\[ \text{Interest in month } k = \text{Remaining Principal at month } k \times \text{Monthly Interest Rate} \]
\[ \text{Remaining Principal at month } k = \text{Total Loan} - (k-1) \times \text{Monthly Principal Repayment} \]
\[ = 360,000 - (k-1) \times 1000 \]

Thus, the monthly payment for month \( k \) (consisting of principal and interest) is:
\[ \text{Monthly Payment}_k = \text{Monthly Principal Repayment} + \text{Interest in month } k \]
\[ = 1000 + \left(360,000 - (k-1) \times 1000\right) \times 0.005 \]
\[ = 1000 + (360 - 0.005k + 0.005) \times 1000 \]
\[ = 1000 + 1800 - 5k + 5 \]
\[ = 2800 - 5k \]

Thus, the formula for the monthly payment in month \( k \) is \( 2800 - 5k \).

**Final Answer:**
The correct formula to determine the monthly payment in month \( k \) is \( 2800 - 5k \), which matches one of the options provided in your quiz question.

Would you like more details on any part of this explanation or have any other questions on this topic?

**Related Questions:**
1. How would the formula change if the interest rate were different?
2. What happens to the total amount paid over the life of the loan if the loan term is shortened?
3. Can you explain how amortization works for different types of loans like fixed and variable rates?
4. What would be the impact on monthly payments if the loan amount were increased?
5. How does the total interest paid change as the loan duration changes?

**Tip:**
Remember, in a linear loan, the principal repayment portion is always constant, while the interest portion decreases as the principal is paid down. This results in decreasing monthly payments over the term of the loan.

Een bedrijf wil een nieuw depot financieren met een hypothecaire lening met een looptijd van 30 jaar. Bank 1 biedt een lineaire lening aan van 360.000 euro tegen een jaarlijkse nominale rente van 6%. Aan het eind van elke maand vindt een betaling (aflossing en rente) plaats. Met welke formule kan je het maandbedrag in maand k bepalen?

Learn how to calculate the monthly payment for a linear loan of €360,000 with a 30-year term and a 6% annual nominal interest rate. This involves using the formula: 2800 - 5k, where k is the month number.

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