Question

# 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?

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## Answer to a math question 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?

Darrell
4.5
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.

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