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3 years ago

8

Suppose that you borrow $13,000 for three years at 5% toward the purchase of a car. Use

20%3D%20%5Cfrac%7BP%5Cfrac%7Br%7D%7Bn%7D%7D%7B1-%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E-%7D" id="TexFormula1" title="PMT = \frac{P\frac{r}{n}}{1-(1+\frac{r}{n})^-}" alt="PMT = \frac{P\frac{r}{n}}{1-(1+\frac{r}{n})^-}" align="absmiddle" class="latex-formula"> to find the monthly payments and the total interest for the loan.

1 answer:

Neko [114]3 years ago

3 0

Answer:

PMT is 389.62

Total interest for the loan is $ 1026.32

Step-by-step explanation:

Given formula of monthly payment,

$PMT=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}$

Where,

P = Present value of the loan,

r = annual rate of interest,

n = number of months in a year,

t = number of years,

Here, P = $13,000, n = 12 months, r = 5% = 0.05, and t = 3 years,

Hence, the monthly payment,

$PMT=\frac{13000\times \frac{0.05}{12}}{1-(1+\frac{0.05}{12})^{-36}}$

≈ 389.62,

Therefore,

The amount of total interest paid = PMT × nt - P

= 389.62 × 36 - 13000

= 14026.32 - 13000

= $ 1026.32

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Consider the triangle A(4,0), B(-2,4), C(0,6)<br> What will be the equation of the altitude BM?

katovenus [111]

Answer:

BM: <u>y = (2/3) x + 16/3</u> with segment length of 2.77

Step-by-step explanation:

AC formula: m = (6-0)/(0-4) = -3/2

(y-0)/(x-4) = -3/2 y = (-3/2)x + 6 ... (1)

BM slope: BM⊥ AC m = 2/3

BM formula: (y-4) / (x- -2) = (y-4) / (x+2) = 2/3

y-4 = 2/3 x + 4/3

<u>y = (2/3) x + 16/3</u> ... (2) -2≤x≤0.31

intercept of AC and BM (M) from (1) and (2): (-3/2)x + 6 = (2/3) x + 16/3

(13/6) x = 2/3 x = (2/3) / (13/6) = 4/13 ≈ 0.31

y = (2/3) (4/13) + (16/3) = (8/39) + (208/39) = 216/39 = 72/13 ≈ 5.54

M (4/13 , 72/13) or (0.31 , 5.54)

segment BM = √(4/13 - -2)² + (72/13 - 4)² = √1300/169 = 2.77

4 0

3 years ago

A puppy named Chance started out at 4 pounds and gained 1 pound every month. At how many months did Chance weigh 13 pounds?

frozen [14]

It should of taken him 9 months to grow from 4 to 13

8 0

4 years ago

HELPPP , me with this please !

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

1/6(1/6)=1/36

3 0

3 years ago

Read 2 more answers

Mr and mrs. Dorsey and their three children are fling to Springfield. The cost of each ticket is $179. Estimate how much the tic

Soloha48 [4]

<span>First figure out how many people there are all together. So mrs and mr is 2 there three children so 2+3=5 so next round 179 to 200 and multiply 200x5. To do that you can use the mental math way witch would be to take the whole number out of 200 and make it 2. Then take the 5 in 200x5 and multiply 2x5. Then add the 2 zeros there were. And your estamated answer would be 1,000.
2+3=5
179=200
200x5
2x5=10
1,000
To figure out your real answer you will have to take 179 and multiply it by 5 so it will look like this:
34
179
x
5
895
Soto conculde the answer would be:

Estamated: $1,000

Exact: $895

Hope this helps!</span>

7 0

3 years ago

alisha [4.7K]

Question:

Consider ΔABC, whose vertices are A (2, 1), B (3, 3), and C (1, 6); let the line segment AC represent the base of the triangle.

(a) Find the equation of the line passing through B and perpendicular to the line AC

(b) Let the point of intersection of line AC with the line you found in part A be point D. Find the coordinates of point D.

Answer:

$y = \frac{1}{5}x + \frac{12}{5}$

$D = (\frac{43}{26},\frac{71}{26})$

Step-by-step explanation:

Given

$\triangle ABC$

$A = (2,1)$

$B = (3,3)$

$C = (1,6)$

Solving (a): Line that passes through B, perpendicular to AC.

First, calculate the slope of AC

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$A = (2,1)$ --- $(x_1,y_1)$

$C = (1,6)$ --- $(x_2,y_2)$

The slope is:

$m = \frac{6- 1}{1 - 2}$

$m = \frac{5}{-1}$

$m = -5$

The slope of the line that passes through B is calculated as:

$m_2 = -\frac{1}{m}$ --- because it is perpendicular to AC.

So, we have:

$m_2 = -\frac{1}{-5}$

$m_2 = \frac{1}{5}$

The equation of the line is the calculated using:

$m_2 = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

$m_2 = \frac{1}{5}$

$B = (3,3)$ --- $(x_1,y_1)$

$(x_2,y_2) = (x,y)$

So, we have:

$\frac{1}{5} = \frac{y - 3}{x - 3}$

Cross multiply

$5(y-3) = 1(x - 3)$

$5y - 15 = x - 3$

$5y = x - 3 + 15$

$5y = x +12$

Make y the subject

$y = \frac{1}{5}x + \frac{12}{5}$

Solving (b): Point of intersection between AC and $y = \frac{1}{5}x + \frac{12}{5}$

First, calculate the equation of AC using:

$y = m(x - x_1) + y_1$

Where:

$A = (2,1)$ --- $(x_1,y_1)$

$m = -5$

So:

$y=-5(x - 2) + 1$

$y=-5x + 10 + 1$

$y=-5x + 11$

So, we have:

$y=-5x + 11$ and $y = \frac{1}{5}x + \frac{12}{5}$

Equate both to solve for x

i.e.

$y = y$

$-5x + 11 = \frac{1}{5}x + \frac{12}{5}$

Collect like terms

$-5x -\frac{1}{5}x = \frac{12}{5} - 11$

Multiply through by 5

$-25x-x = 12 - 55$

Collect like terms

$-26x = -43$

Solve for x

$x = \frac{-43}{-26}$

$x = \frac{43}{26}$

Substitute $x = \frac{43}{26}$ in $y=-5x + 11$

$y = -5 * \frac{43}{26} + 11$

$y = \frac{-5 *43}{26} + 11$

Take LCM

$y = \frac{-5 *43+11 * 26}{26}$

$y = \frac{71}{26}$

Hence, the coordinates of D is:

$D = (\frac{43}{26},\frac{71}{26})$

3 0

3 years ago