The Bauer family wants to build a house and needs to take out a loan of €120,000. They get offers for a possible loan agreement from two banks and receive the following information Bank A offers you to pay off the loan agreement in installments within 4 years at 3.4% per year Bank b offers to repay the loan amount within 3 years at 3.5% per year For each of the offers, calculate the annual remaining debt, repayments to be made, interest and annuity. Which offer is more attractive?

Consider the loan agreement with Bank A:
Loan amount, \( P = €120,000 \)
Annual interest rate, \( r = 3.4\% = 0.034 \)
Loan term, \( t = 4 \)
Using the formula for calculating the annuity \[ A = P \frac{r(1+r)^t}{(1+r)^t-1} \]:
A = 120,000 \frac{0.034(1+0.034)^4}{(1+0.034)^4-1}
A = 120,000 \frac{0.034(1.034)^4}{(1.034)^4-1}
A = 120,000 \frac{0.034 \cdot 1.139267}{1.139267-1}
A = 120,000 \frac{0.038734}{0.139267}
A = 120,000 \cdot 0.278095
A = 33,371.44
Total repayment after 4 years:
4 \cdot 33,371.44 = 133,485.76
Total interest paid:
133,485.76 - 120,000 = 13,485.76

Consider the loan agreement with Bank B:
Loan amount, \( P = €120,000 \)
Annual interest rate, \( r = 3.5\% = 0.035 \)
Loan term, \( t = 3 \)
Using the formula for calculating the annuity \[ A = P \frac{r(1+r)^t}{(1+r)^t-1} \]:
A = 120,000 \frac{0.035(1+0.035)^3}{(1+0.035)^3-1}
A = 120,000 \frac{0.035(1.035)^3}{(1.035)^3-1}
A = 120,000 \frac{0.035 \cdot 1.108086}{1.108086-1}
A = 120,000 \frac{0.038783}{0.108086}
A = 120,000 \cdot 0.359126
A = 43,095.20
Total repayment after 3 years:
3 \cdot 43,095.20 = 129,285.60
Total interest paid:
129,285.60 - 120,000 = 9,285.60

Comparing total interest paid:
- Bank A: \( 13,485.76 \)
- Bank B: \( 9,285.60 \)

Thus, Bank B is more attractive with lower total interest.