Question

Question 8 10 pts 8) You want to buy a house and can pay a 564,000 down payment and a mortcake payment of $1.800 each month. Thirty year mortgage loans are available for 9% per year. What is the most expensive house you can buy? 3 IVA -A- IEE 3 1 . x , EE - ² x G T To 12pt. - Paragraph - MacBook Pro

Answer 1

Hey there stay safe and stay home.

Down payment = $64000

Monthly payment x=$1800

Time t=30 y

Interest r= 9%

The Cost of the house except Down payment P =?

The formula we use is,

$P(1+\frac{\frac{r}{12}}{100})^{12t}= x\times \frac{(1+\frac{\frac{r}{12}}{100})^{12t}-1}{\frac{\frac{r}{12}}{100}}\\ \\ \Rightarrow P(1+\frac{\frac{9}{12}}{100})^{360}= x\times \frac{(1+\frac{\frac{5}{12}}{100})^{360}-1}{\frac{\frac{9}{12}}{100}}\\ \\ \Rightarrow P(1.0075)^{360}= 1800\times \frac{1.0075^{360}-1}{.0075}\\ \\ \Rightarrow P= 1800\times \frac{1.0075^{360}-1}{.0075\times (1.0075)^{360}}=223707.3582\approx 223707$

So total value of the house is

$( 223707 + 64000) = $287707

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