Question : Find if the coordinates given lie on the circles below: (a) Does (4,2) lie on the circle with equation

Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo

svp [43]

Answer:

Step-by-step explanation:

From the given information:

The present value of the house = 128000

interest rate compounded monthly r = 7.8% = 0.078

number of months in a year n= 12

duration of time t = 30 years

To find their regular monthly payment, we have:

$PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}$

$128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

128000 = 138.914 P

P = 128000/138.914

P = $921.433

∴ Their regular monthly payment P = $921.433

To find the unpaid balance when they begin paying the $1400.

when they begin the payment ,

t = 30 year - 5years

t= 25 years

$PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

PV = $121718.2714

C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:

$121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}$

$121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}$

$0.60859 = (0.006458)^{nt}$

$nt = \dfrac{0.60859}{0.006458}$

nt = 94.238 payments is required to pay off the loan.

How much interest will they save by paying the loan using the number of payments from part (c)?

The total amount of interest payed on $921.433 = 921.433 × 30(12) years

= 331715.88

The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)

= 177795.38

The amount of interest saved = 331715.88 - 177795.38

The amount of interest saved = $153920.5

6 0

4 years ago

HELP THIS IS IMPORTANT!!! The range of the following relation R {(3.-5), (1, 2), (-1,-4),(-1, 2)} is (1 point) Oa ng 1-1.1.3) Ob

garri49 [273]

Answer:

The range is -5,2,-4,

Step-by-step explanation:

hope that helps

4 0

3 years ago

PLEASE HELP!! Need help with my homework!

gulaghasi [49]

Answer:

Line segment: AD (without arrow)

Ray: BA (with one sided arrow)

Rays with common endpoint: AC and AD (with one sided arrow)

Intersection: AE (double sided arrow)

Collinear points: B, A, C

PLEASE MARK AS BRAINLIEST

6 0

3 years ago

Mcm de 12 21 63 <br> Encontrar el resultado

emmasim [6.3K]

Answer:

Lo mcm es 252.

Step-by-step explanation:

El objetivo de esta queston es encontrar el mínimo multiplo comun de estes tres numeros.

Para eso, factoramos estes numeros en valores primos, e despues multiplicamos estos factores.

12 21 63

12 - 21 - 63|2

6 - 21 - 63|2

3 - 21 - 63|3

1 - 7 - 21|3

1 - 7 - 7|7

1 - 1 - 1

2*2*3*3*7 = 252

Lo mcm es 252.

6 0

3 years ago

The Winners' Circle sportswear and equipment store bought a baseball glove from DOCK's Sporting Goods for $66.00. They want to m

dsp73

Answer:

Correct answer is : $220

Step-by-step explanation:

Here, cost price = $66

Let the selling price be $x.

According to the statement given in problem,

Selling price - cost price = 70% of selling price

i.e. x - 66 = 70% * x

x - 70x/100 = 66

30x / 100 = 66

x = 6600 / 30 = $220

i.e Selling price = $220

7 0

3 years ago