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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Darrell

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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.

Loan amount, \( P = €120,000 \)

Annual interest rate, \( r = 3.4\% = 0.034 \)

Loan term, \( t = 4 \)

Using the formula for calculating the annuity \[ A = P \frac{r(1+r)^t}{(1+r)^t-1} \]:

Total repayment after 4 years:

Total interest paid:

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 \[ A = P \frac{r(1+r)^t}{(1+r)^t-1} \]:

Total repayment after 3 years:

Total interest paid:

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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