What is the next term for the given arithmetic sequence?<br><br> -3, -2.25, -1.5, -0.75, ...

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

This number was rounded to the nearest hundred thousand. List the possible digits that could go in the ten thousands place to ma

aleksklad [387]

The possible digits could be 0, 1, 2, 3, or 4 as they would cause the entire number to round down instead of up.

6 0

3 years ago

Read 2 more answers

The range for the set of data represented by the following box-and-whisker plot is 8.

DIA [1.3K]

Answer:

True

Step-by-step explanation:

<u>The range is the difference between the lowest and the highest values of the set:</u>

19 - 11 = 8

The answer is TRUE

3 0

2 years ago

Read 2 more answers

ASAP HELP ME plz wit this

Lina20 [59]

Answer:

Step-by-step explanation:What??

5 0

2 years ago

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a

jeka94

Answer:

0.2 or 20%

Step-by-step explanation:

If the times of arrival vary uniformly, there is an equal chance of an employee reporting at any given time between 8:40 and 9:30.

The range between 8:40 and 9:30 is 50 minutes.

The range between 9:00 and 9:10 is 10 minutes.

Therefore, the probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:

$P(9:00\leq X\leq 9:10)=\frac{10}{50}=0.20=20\%$

The probability is 0.2 or 20%.

6 0

3 years ago

What is the next term for the given arithmetic sequence? -3, -2.25, -1.5, -0.75, ...