# Mortage hypo loan

The Jonáš family decided to buy an older apartment, which cost EUR 30,000. They found EUR 17,000 and took the loan with the bank for the remaining amount. What interest did they receive if they repay this amount for 15 years at EUR 120 per month?

Result

p =  7.431 %

#### Solution:

$a=30000 - 17000=13000 \ \text{eur} \ \\ n=15 \cdot \ 12=180 \ \\ s=120 \ \text{eur} \ \\ \ \\ b=n \cdot \ s=180 \cdot \ 120=21600 \ \text{Eur} \ \\ \ \\ s=a \cdot \ \dfrac{ q^n \cdot \ (q-1) }{ q^n-1 } \ \\ \ \\ 120=13000 \cdot \ \dfrac{ q^{180} \cdot \ (q-1) }{ q^{180}-1 } \ \\ q>0 \ \\ q=1.0061922243045 \doteq 1.0062 \ \\ p_{1}=q-1=1.0062-1 \doteq 0.0062 \ \\ p_{2}=12 \cdot \ p_{1}=12 \cdot \ 0.0062 \doteq 0.0743 \ \\ \ \\ \ \\ p=100 \cdot \ p_{2}=100 \cdot \ 0.0743 \doteq 7.4307 \doteq 7.431 \%$

Equation is non-linear.

## The real roots of the equation:

q1 = -0.97217199735518
q2 = -0.97061681742462
q3 = 1.0061922243045

Calculated by our simple equation calculator.

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