The Taylors have purchased a $190,000 house. They made an initial down payment of $30,000 and secured a mortgage with interest charged at the rate of 7%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)
Answers
The Taylors' monthly mortgage payment is approximately $1,064.49. After 5, 10, and 20 years, their equity is approximately $55,474.34, $86,913.18, and $138,082.63, respectively.
To calculate the monthly payment for the mortgage, we can use the formula for an amortizing loan:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate
n = Total number of payments
Given:
Loan amount (P) = $160,000
Interest rate = 7% per year
Number of payments (n) = 30 years * 12 months/year = 360
First, we need to calculate the monthly interest rate (r):
Monthly interest rate = (Annual interest rate) / (Number of months in a year)
r = 7% / 12 = 0.07 / 12 = 0.00583
Now, we can calculate the monthly payment (M):
M = $160,000 * 0.00583 * (1 + 0.00583)^360 / ((1 + 0.00583)^360 - 1)
M ≈ $1,064.49
Therefore, the Taylors will be required to make a monthly payment of approximately $1,064.49.
To calculate the equity after 5, 10, and 20 years, we need to determine the remaining loan balance after each specific time period.
We can use an amortization table or a loan amortization calculator to calculate the remaining balance.
After 5 years:
Number of payments = 5 years * 12 months/year = 60 payments
Remaining loan balance = Balance after 5 years ≈ $134,525.66
After 10 years:
Number of payments = 10 years * 12 months/year = 120 payments
Remaining loan balance = Balance after 10 years ≈ $103,086.82
After 20 years:
Number of payments = 20 years * 12 months/year = 240 payments
Remaining loan balance = Balance after 20 years ≈ $51,917.37
To calculate the equity, we subtract the remaining loan balance from the initial house value ($190,000):
Equity after 5 years ≈ $190,000 - $134,525.66 ≈ $55,474.34
Equity after 10 years ≈ $190,000 - $103,086.82 ≈ $86,913.18
Equity after 20 years ≈ $190,000 - $51,917.37 ≈ $138,082.63
Therefore, after 5 years, the Taylors' equity is approximately $55,474.34. After 10 years, the equity is approximately $86,913.18. After 20 years, the equity is approximately $138,082.63.
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Related Questions
Find the midpoint of the segment with the following endpoints.
(1,7) and (10,4)
Answers
Step-by-step explanation:
from midpoint formula P(x,y)=1+10÷2 , 7+4÷2
=11÷2 ,11÷2
= 5.5 ,5.5
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Using compound interest formula, the amount compounded at a rate of 3% quarterly for 5 years is $15,095.39
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeplugging the values into the formula above
A = 13000(1 + 0.03/4)^4 * 5
A = 13000(1.0075)^20
A = $15,095.39
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x and y are both bigger than 30. x and y have HCF 21 and LCM 1617. Find x and y.
Answers
The values of x and y are 99 and 343
The HCFThe HCF of numbers is the highest common factors of the numbers
The LCMThe LCM of numbers is the lowest common multiple of the numbers
The HCF and the LCM are given as:
\(HCF = 21\)
\(LCM = 1617\)
Multiply the HCF and the LCM
\(HCF \times LCM = 21 \times 1617\)
\(HCF \times LCM = 33957\)
The product of the numbers x and y equals the product of the HCF and the LCM.
So, we have:
\(x \times y = 33957\)
Prime FactorsExpress 33957 as a prime factor
\(x \times y = 3^2 \times 7^3 \times 11\)
Rewrite the equation as
\(x \times y = 99 \times 7^3\)
\(x \times y = 99 \times 343\)
By comparison:
\(x = 99\)
\(y= 343\)
Hence, the values of x and y are 99 and 343
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Two angles are supplementary. One measures 7x - 9 and the other measures 4x + 3. Find x and the measure of the smaller angle
Answers
Answer:
Supplementary angles add up to 180°
180=7x-9+4x+3
180=7x+4x-9+3
180=11x-7
180+7=11x
187=11x
11x=187
x=187/11
x=17
Therefore x = 17
What is the quotient of 8.44 and 0.04?
10 pts
Answers
8.44/0.04=211
hope this helps!
Answer:
211
Step-by-step explanation:
8.44 divided by 0.04 = 211
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area in square centimeters?
Answers
Answer:
Area= 48 cm
Step-by-step explanation:
:)
Using a 2-year moving average, the forecast for year 6=3825 miles (round your response to the nearest whole number). b) If a 2-year moving average is used to make the forecast, the MAD based on this = miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.45 and 0.55 (the weight of 0.55 is for the most recent period) = whole number).
Answers
The forecast for year 6 using a 2-year moving average is 3825 miles.
The MAD based on the 2-year moving average cannot be calculated without the actual data for years 5 and 4.
The forecast for year 6 using a weighted 2-year moving average cannot be determined without the specific values for years 5 and 4.
A 2-year moving average involves taking the average of the data for the current year and the previous year to make the forecast for the next year. In this case, the forecast for year 6 is determined by averaging the data for years 5 and 4. The resulting forecast is 3825 miles.
To calculate the Mean Absolute Deviation (MAD), we need three years of matched data. However, the provided information only mentions the forecast for year 6 without mentioning the actual data for years 5 and 4. Therefore, the MAD value cannot be determined without the actual data.
In the case of a weighted 2-year moving average, the weights assigned to the data for the two years determine their relative importance in the forecast. The weight of 0.45 is assigned to the less recent period, and the weight of 0.55 is assigned to the most recent period. However, the specific values for years 5 and 4 are not provided, making it impossible to calculate the forecast for year 6 using the weighted moving average.
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Please help me out with this
Answers
Step-by-step explanation:
The correct answer is 946
c=946
Answer:
c = 946
Step-by-step explanation:
771 + 175 = 964
946 -771 =175
Select all equations that have the same solution as 3x-6=18
Answers
It should be noted that the value of x in the expression 3x - 6 = 18 is 8.
How to illustrate the information?It should be noted that an equation is used to show the relationship that exists between the variables that are illustrated.
Based on the information, the expression that's illustrated is given as:
3x - 6 = 18
Collect like terms
3x = 18 + 6.
3x = 24
Divide
x = 24 / 3
x = 8
Therefore, it should be noted that the value of x in the expression 3x - 6 = 18 is 8.
Note that the information was incomplete but the question was solved accordingly.
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thankssss plzzz helpp
Answers
2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0,y1,y2,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]βtln(ct) with β(<1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1 and c3 are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!
Answers
a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. U0 = ∑t=0[infinity](β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.
a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:
At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.
Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin
d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity](β(1 + r))^tln(ct).
This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.
This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.
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A hat contains four balls. The balls are numbered 2, 4, 4, and 5. One ball is randomly selected and not replaced, and then a second ball is selected. The numbers on the two balls are added together.A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using the sum of the numbers on the balls. The sizes are small, medium and large.Which description accurately explains how a fair decision can be made in this situation
Answers
The description that accurately explains how a fair decision can be made in this situation is : IF a ball with number 4 and 5 are picked you order the largest size, if a ball with number 4 and another with number 4 is picked you order the medium size, but if the balls picked are that of number 2 and 4, then you order a small size. The probability of each result occurring is a fair one.
Meaning of probability and full workingProbability is the degree of occurrence of an event. it can also be said to be the chance for an event to occur.
Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.
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Why do we use p hat in statistics?
Answers
In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.
The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.
Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.
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35 POINTS
Find the range of this quadratic function
Answers
Answer:
The range of this quadratic function is
-infinity < y ≤ 2.
21. Water that is sprayed upward from a
sprinkler with an initial velocity of
20 m/s can be approximated by the
function y=-5x² + 20x, where y is
the height of a drop of water x seconds
after it is released. Graph this function.
Find the time it takes a drop of water
to reach its maximum height, the
water's maximum height, and the time
it takes the water to reach the ground.
Answers
Answer:
2 seconds to maximum height20 meters maximum height4 seconds to reach the groundStep-by-step explanation:
The function can be graphed using a graphing calculator, geometry app, or spreadsheet. One such graph is attached. Often, these tools are capable of identifying extrema and intercepts.
__
extremeThe vertex of the graph is reported as (x, y) = (2, 20). This means the maximum height is reached after 2 seconds. That maximum height is 20 meters.
__
interceptThe drop is launched from ground level at x = 0 seconds. It returns to ground level at x = 4 seconds.
pls help me thank you
Answers
Answer:
x=75
Step-by-step explanation:
Answer:
x=75
Step-by-step explanation:
parralel angles
90 - 15 = 75
On an English test, John scored 50 points on the essay portion. The test also had short-answer questions worth 2.5 points each. Choose an expression for John’s total points if he answered r short-answer questions correctly.
Answers
Answer:
2.5x+50
Step-by-step explanation:
r = numbers of right answers
Points the essay worth = 50
2.5 = points each right short answer
Which situation is best represented by the following equation?
45w + 123.95 = 753.95
Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?
Erica paid $75 3.95 for dance classes. She paid $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?
Answers
Answer:
The first one, 14 weeks of dance classes.
Step-by-step explanation:
She paid $753.95 as a total for all of the classes, not just one week. She paid her registration free, which you subtract from 753.95 to get 630.00. She pays 45 per week, so you divide 630 by 45 to get the amount of weeks she attended dance classes, or 14 weeks.
im running out of things to say
Answers
Answer:
i think its b
Step-by-step explanation:
3(x+1)+6=-9 what is x
Answers
Answer:
x= -6
Step-by-step explanation:
Distribute 3x+3+6=-9
Add 3x+9=-9
Subtract 3x+9-9=-9-9
Simplify 3x=-18
Divide 3x/3=-18/3
Simplify x=-6
Three times the quantity of a number increased by 4 is -9. Write the equation and solve
Answers
The value of the number is -13/3
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of arithmetic operations such as subtraction, multiplication, division, addition, bracket and parentheses.
These expressions are also made up of variables, terms, coefficients, constants and factors.
From the information given, we have that;
The number = x
3x + 4 = -9
collect like terms
3x = -9 - 4
subtract the like terms
3x = -13
Make 'x' the subject
x = -13/3
Hence, the value is -13/3
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I NEED HELP PLEASE, THANKS! :)
Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth. (SHOW WORK)
Answers
Answer: 123.6 units²
Step-by-step explanation:
Since it is an isosceles triangle, we can draw a median from the ap ex (b) to the base (ac) to create a right triangle at point (d). Then we can use the Pythagorean Theorem to find the height (bd) of the triangle.
(dc)² + (b d)² = (bc)²
7² + (b d)² = 19²
(b d)² = 19² - 7²
(b d)² = 312
b d = 17.66
A = (1/2) base x height
= (1/2) ac x b d
= (1/2) 14 x (17.66)
= 7(17.66)
= 123.6
Dave is driving from Portola Ave. To Springs Street. Portola Ave. Is marked as "A" and Springs Street is marked as "E".
He takes 3 miles to go to the ice store. (C)
He drives back to Portola Ave. Where his house is.
From A to C is 6 miles
After a few hours he drives to the market (D)
he spends 25 minutes there and drives back home which is 24 miles.
He stops by a gas station (B) when he goes back home. He takes 10 minutes there.
Then when he’s home, he packs items which takes 55 minutes.
Then he drives to springs street (E)
This takes 40 miles.
He realized that he forgot something at the market, so he drives back to the market which is 5 miles away.
Then he drives back to Springs Street
After he enters the airport (E) he takes 25 minutes to have his luggage checked and boards the plane. Then the plane immediately takes off.
It is 12:45pm when Dave is about to go the ice store.
When he rests for a few hours after coming back from ice store he rests for 2 hours.
What time does the plane take off?
Answers
When he rests for a few hours after coming back from ice-store he rests for 2 hours the time the plane takes off is 9:10 pm.
Total distance traveled is 151 miles.
Dave spends 25 + 10 + 55 + 25 = 115 minutes (or 1 hour and 55 minutes) on stops.
Dave rests for 2 hours.
To calculate the time the plane takes off, we need to add up all the time Dave spends on driving, stops, and rests, and then add that time to the time he starts (12:45 pm).
Time to drive from A to C and back to A: 2 * 6 / 60 = 0.2 hours
Time to drive from A to C to D to B to A: (6 + 24 + 24 + 3) / 60 = 0.95 hours
Time to drive from A to C to D to home to E to market to E: (6 + 24 + 24 + 40 + 5 + 5) / 60 = 2.33 hours
Time to rest: 2 hours
Total time spent: 0.2 + 0.95 + 2.33 + 1.92 = 5.4 hours
Time of departure: 12:45 pm + 5.4 hours = 6:25 pm
Adding 45 minutes for the luggage check and boarding, the plane takes off at 6:25 pm + 0.45 hours = 7:10 pm
Adding another 2 hours for the time zone difference, the plane takes off at 7:10 pm + 2 hours = 9:10 pm.
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PLEASE HELP MEEEE
Beatrice threw a stone one and seven fourteenths yards. Tilly threw a stone nine fourteenths of a yard. What is a reasonable estimate of the difference between their two throws?
1 yard
one and one half yards
2 yards
two and one half yards
Answers
Answer: About 1 yard is a reasonable estimate.
Step-by-step explanation:
1 ⁷/₁₄ is a yard and a half
⁹/₁₄ is just a bit more than half a yard
Rounding that off to half a yard, and finding the difference leaves about 1 yard.
The actual difference is ¹²/₁₄ of a yard the same as ⁶/₇ of a yard, or just about 5¹/₂ inches less than a yard.
randomly select a point inside a triangle with side lengths 5, 12, and 13, then the probability that the distance from this point to the nearest vertex of the triangle is less than 2 is
Answers
The probability that a randomly selected point inside a triangle with side lengths 5, 12, and 13 has a distance from the nearest vertex of the triangle less than 2 is approximately 0.4286, or 42.86%.
To find the probability, we can consider the triangle with side lengths 5, 12, and 13 as a right triangle, where the side length 13 represents the hypotenuse. Let's assume the vertices of the triangle are A, B, and C, with AB = 5, AC = 12, and BC = 13.
First, we calculate the area of the triangle using Heron's formula, which gives us √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle and a, b, and c are the side lengths. In this case, s = (5+12+13)/2 = 15.
Using the formula, the area of the triangle is \(\sqrt{15(15-5)(15-12)(15-13)} = \sqrt{15 \cdot 10 \cdot 3 \cdot 2} = \sqrt{900} = 30\).
Now, let's consider the smaller triangle formed by the original triangle's vertices and a point P inside it. To calculate the probability, we need to find the area of the region where the distance from P to the nearest vertex is less than 2.
If we draw circles centered at each of the vertices A, B, and C with radius 2, the area enclosed by these circles within the triangle represents the region we are interested in.
Calculating the areas of these circles, we find that each circle has an area of 4π. Since there are three circles, the total area of the enclosed region is 3 × 4π = 12π.
Therefore, the probability that a randomly selected point inside the triangle has a distance from the nearest vertex less than 2 is given by (12π / 30) = (2π / 5), which is approximately 0.4286 or 42.86%.
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Last Friday Mary had $28 over the weekend she received some money for washing the dog she now has $42 how much money does she receive
Answers
Answer:
14
Step-by-step explanation:
42-28
A bag of rare spice that weighs 2/3 pounds will be split equally among 12 people. How much spice will each person get
Answers
Answer:
1/18 pound each
Step-by-step explanation:
Take the number of pounds and divide by 12 people
2/3 ÷12
Copy dot flip
2/3 * 1/12
Rewriting
2/12 * 1/3
1/6 * 1/3
1/18 pound each
Answer:
Each person will get 1/18 pounds of spice from the bag
Step-by-step explanation:
Divide 2/3 by 12:
Make 12 a fraction by adding 1 as the denominator:
2/3 ÷ 12/1
Reciprocate the second fraction:
2/3 ÷ 1/12
Turn it into multiplication:
2/3 x 1/12 = 2/36
SIMPLIFY 2/36:
2/36
Divide both sides by 2:
1/18
so your answer is 1/18
I hope I helped!
determine if the equation is exact. if it is, then solve it. (3x^2y 3)dx (x^3-5)dy=0
Answers
Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
for function
Φ(x) = x^m
then
dΦ/dx (x) = m*x^(m-1)
d²Φ/dx² (x) = m*(m-1)*x^(m-2)
then
for a expression
3x^2 (d^2y/dx^2) + 11x(dy/dx) - 3y = 0
3x^2*m*(m-1)*x^(m-2) + 11*x* m*x^(m-1) - 3*x^m = 0
3*m*(m-1)*x^m + 11*m*x^m- 3*x^m = 0
dividing by x^m
3*m*(m-1) + 11*m - 3 =0
3*m² + 8 m - 3 =0
m= [-8 ± √(64 + 4*3*3)]/2 = (-8±10)/2
m₁ = -9 , m₂= 1
then Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1
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Which postulate or theorem proves that these two triangles are congruent
Answers
Answer:
AAS
ANGLE ANGLE SIDE.........
In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz? m∠x m∠z < 90° m∠y > 90° ∠x and∠y are complementary m∠x m∠y < 90°
Answers
m∠X + m∠Y < 90° is true.
How to solve it?XYZ is a triangle.
We have to find the option that is true about △XYZ.
By angle sum property of a triangle,
The sum of all the interior angles of a triangle is always equal to 180°.
So, ∠X + ∠Y + ∠Z = 180°
Given, m∠Z > m∠X + m∠Y.
This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.
so, ∠X + ∠Y must be less than 90°.
Hence, we can say that ∠X + ∠Y < 90°
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Answer: Option 4 or D. m∠x + m∠y∠90°
Step-by-step explanation: Trust Me! It is correct on Edge!
Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?
A: D. m∠x + m∠y∠90°