Mathematics, 21.07.2019 23:30 katlynnschmolke

Vanessa can afford a $1405-per-month house loan payment. if she is being offered a 20-year house loan with an apr of 4.8%, compounded monthly, which of these expressions represents the value of the most money she can borrow?

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To solve this we are going to use the present value formula: $PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ]$
where

is the present value

is the periodic payment

is the interest rate in decimal form

is the number of times the interest is compounded per year

is the number of payments per year

is the number of years

We know for our problem that she can afford a $1405-per-month house loan payment, so P=1405

and

. We also know that the loan is a 20-year house loan, so t=20

. To convert the interest rate to decimal form, we are going to divide the rate by 100% $r= \frac{4.8}{100}=0.048$ . Since the interest rate is compounded monthly, it is compounded 12 times per year; therefore, n=12

. Lets replace those values in our formula:

$PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ]$
$PV=1405[ \frac{1-(1+ \frac{0.048}{12})^{-(12)(20)} }{ \frac{0.048}{12} } ]$
PV=216501.09

We can conclude that the expression that represents the value of the most money she can borrow is: $PV=1405[ \frac{1-(1+ \frac{0.048}{12})^{-(12)(20)} }{ \frac{0.048}{12} } ]$ . Evaluating the expression we can prove that she can borrow $216,501.09

Answer from: Quest

image result for what is another name for consecutive interior angles?

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

Answer from: Quest

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