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olga2289 [7]
4 years ago
12

Shelley purchased a home in Maryland Heights, MO, for $204,000. Her down payment was 20% of the cash price, and she obtained a m

ortgage for 20 years at 7%. What's Shelley's monthly payment?
Mathematics
1 answer:
Mkey [24]4 years ago
3 0
To solve this we are going to use the loan payment formula: P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} }
where
P is the payment
PV is the present debt
r is the interest rate in decimal form 
n is the number of payments per year 
t is the time in years 

Since she paid 20% of the value of the home, PV=204000-(240000)20%=163200
Now, to convert the interest rate to decimal form, we are going to divide the rate by 100% r= \frac{7}{100} =0.07. Since we are finding Shelly's monthly payment and a year has twelve months, n=12. We also know that t=20, so lets replace those values in our formula:
P= \frac{ \frac{r}{n}(PV)}{1-(1+ \frac{r}{n})^{-nt} }
P= \frac{ \frac{0.07}{12}(163200)}{1-(1+ \frac{0.07}{12})^{-(12)(20)} }
P=1265.29

We can conclude that Shelly's monthly payment is $1265.29
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The remainder from the division of the algebraic equation is -53/8.

<h3>What is the remainder of the algebraic expression?</h3>

The remainder of the algebraic expression can be determined by using the long division method.

Given that:
\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}

where:

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Using the long division method, we have:

\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}

\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}

\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}

\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}

Therefore, we can conclude that the remainder is -53/8.

Learn more about the division of algebraic equations here:

brainly.com/question/4541471

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