You plan to remodel the bathroom in your apartment and decide to take out a mortgage loan of €12 000. The bank offers you an interest rate of 4.2% p.a. with a monthly repayment of €250. After 3 years, you decide to make a special repayment of €2 000 and ask for an adjustment of the repayments so that the remaining principal and loan are repaid in exactly 1 year.

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

b) By how much percent is the new installment lower/higher than the original one?

c) What percentage of that year's loan was the extra payment?

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

You plan to remodel the bathroom in your apartment and decide to take out a mortgage loan of €12,000. The bank offers you an interest rate of 4.2% p.a. with a monthly repayment of €250. After 3 years, you decide to make a special repayment of €2,000 and ask for an adjustment of the repayments so that the remaining principal and loan are repaid in exactly 1 year.

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

b) By how much percent is the new installment lower/higher than the original one?

c) What percentage of that year's loan was the extra payment?

Learn how to calculate the outstanding balance of a €12,000 loan after 3 years with an interest rate of 4.2%, monthly repayments of €250, and a special repayment of €2,000. Understand how the new monthly repayment is adjusted and how to calculate the percentage change in the installment.

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