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Kathy wants to buy a condominium selling for $96,000. The taxes on the property are $1300 per year, and homeowners' insurance is $336 per year. Kathy's gross monthly income is $4000. She haher van. The bank is requiring 20% down and is charging a 9.5% interest rate with no points. Her bank will approve a loan that has a total monthly mortgage payment of principal, interest, property tthan or equal to 28% of her adjusted monthly income. Complete parts a) through h) below.a) Determine the required down payment.The required down payment is $b) Determine 28% of her adjusted monthly income.28% of her adjusted monthly income is $(Round to the nearest cent as needed.)c) Determine the monthly payments of principal and interest for a 25-year loan.The monthly payment of principal and interest for a 25-year loan is $(Round to the nearest cent as needed.)d) Determine her monthly payment, including homeowners' insurance and taxes.Her total monthly payment, including homeowners' insurance and taxes is $(Round to the nearest cent needed.) Does Kathy qualify for the loan?0 YesO No

Sagot :

a) the cost of the house is 96000 and the down paidment is the 20% so we can use a rule of 3 to solve it so:

[tex]\begin{gathered} 96000\to100 \\ x\to20 \end{gathered}[/tex]

so the equation will be:

[tex]\begin{gathered} x=\frac{96000\cdot20}{100} \\ x=19200 \end{gathered}[/tex]

b) her income is $4000 so the 28% will be:

[tex]\begin{gathered} 4000\to100 \\ x\to28 \end{gathered}[/tex]

so the equation will be:

[tex]\begin{gathered} x=\frac{4000\cdot28}{100} \\ x=1120 \end{gathered}[/tex]

c) the equation that models a loan is:

[tex]C=\frac{P\cdot(0.095\cdot(1+0.095)^n)}{(1+0.095)^{25}-1}[/tex]

So we replace the princeiple and find monthly paidment.

[tex]\begin{gathered} C=\frac{76800\cdot(0.095\cdot(1.095)^{25}}{8.67} \\ C=\frac{76800\cdot0.92}{8.67} \\ C=\frac{70540.30}{8.67} \\ C=8136.14 \\ C\approx8136 \end{gathered}[/tex]

d)The total monthly paidment will be:

[tex]\begin{gathered} T=8136+\frac{1300}{12}+\frac{336}{12} \\ T=8136+108.33+28 \\ T=8272.33 \\ T\approx8272 \end{gathered}[/tex]

SOo the answer is NO she can't afort to buy this house

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