Is an arithmetic sequence a function?

tatuchka [14]

5^3 should be the answer. The answer would be 125.

5 0

4 years ago

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

3 years ago

What is the opposite of 4

horsena [70]

Negative 4 or -4 is the answer

8 0

3 years ago

When will these two lines intersect <br>C. y=-2x +3<br>y = x

Andrej [43]

Answer:

The intersection point of the given lines is (1,1).

Step-by-step explanation:

Here, the given equations are:

y = - 2 x + 3

y = x

Substitute y = x in the first equation,

y = -2 x + 3 becomes y = -2 (y) + 3

or, y + 2 y = 3

or, 3 y = 3 ⇒ y = 3/3 = 1

⇒ y = 1

Now, as x = y ⇒ x = 1

Hence, the intersection points of the given lines is (1,1).

8 0

3 years ago

A submarine's position is 600 feet below sea level. It descends 218 feet. What is the submarine's new elevation?

ollegr [7]

Answer with explanation:

If Submarine position is 600 feet below sea level, it can be represented in terms of integers as = - 600

Now , it descends 218 feet ,from where it is presently Located.

Descend in terms of integers can be represented as = - 218 feet

Submarine New position or Elevation = - 600 feet + (-218 feet)

= -818 feet

Option A : -818 feet

6 0

3 years ago

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