1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
velikii [3]
3 years ago
9

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

r 5 years, then decide to pay $1300 per month.
A) Find their regular monthly payment.
B) Find the unpaid balance when they begin paying the $1400.
C) How many payments of $1400 will it take to pay off the loan?
D) How much interest will they save by paying the loan using the number of payments from part (c)?
Mathematics
1 answer:
svp [43]3 years ago
6 0

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

You might be interested in
What does 1/3+1/4 equal to?
bixtya [17]
7/12 u need to multiply 3*4 and u keep the numerator the same
7 0
3 years ago
Which expression are equivalent to 2x+4
Ksivusya [100]

Answer:

2(x+2)

Step-by-step explanation:

Factor out the 2.

4 0
3 years ago
I need help on a McGraw hill assignment its due soon pls help.
blagie [28]

Answer:

1850

Step-by-step explanation:

The problem is asking you how many kids (predicted by the superintendent) will buy lunches for 1-2 days. Since you know the percentage predicted and the student amount, just multiply as a decimal (convert by putting the number over 100 as a fraction.)

5000*0.37=1850

4 0
2 years ago
Read 2 more answers
The Porter family budget in the new city is shown in the graph. Of the seven expenses shown, which of the following is fixed?
barxatty [35]

Answer:

Housing

Step-by-step explanation:

5 0
3 years ago
Which of the following is a solution to the equation y = 3x - 1 ?
Korvikt [17]
One way of determining the answer is by substituting the values to the equation. It is done as follows:

A. (4,1)
<span>y = 3x - 1
</span>1 = 3(4) - 1 = 11 -------> not equal

B. (2,5)
<span>y = 3x - 1
</span>5 = 3(2) - 1 = 5 --------> equal

C. (4,3)
<span>y = 3x - 1
</span>3 = 3(4) -1 --------------> not equal

D. (0, -3)
<span>y = 3x - 1
-3 = 3(0) -1 = -1 ---------> not equal</span>
8 0
3 years ago
Other questions:
  • -wsquared=576. Solve the equation
    12·2 answers
  • Find the area of the trapezoid.<br> 15 m<br> 12 m<br> 18 m<br> D<br> 21 m
    10·1 answer
  • Last Question...Please help if you can...(25 points if you answer this)
    6·1 answer
  • Given the arithmetic sequence an = −4 + 4(n − 1), what is the domain for n? (1 point)
    9·1 answer
  • I need to find the length
    15·1 answer
  • Estimate the value of \frac{\sqrt{2\pi }}{\sqrt{5}}
    12·1 answer
  • Name each angle in four ways.
    10·1 answer
  • Find the sum of 2m and 9m.
    14·1 answer
  • A long year end status report for work is 136 pages long. You need to print 19 copies for a meeting next week. How much is the p
    12·1 answer
  • And the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!