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3 years ago

A couple purchased a home and signed a mortgage contract for $900,000 to

Mathematics

1 answer:

Tema [17]3 years ago

7 0

9514 1404 393

Answer:

$33,336.83
$35,176.68
$36,869.23
$38,266.75
$39,158.08

Step-by-step explanation:

The amortization formula can be used to find the payment value.

A = P(r/2)/(1 -(1 +r/2)^(2n))

where P is the principal amount at the beginning of the loan period, r is the annual interest rate, n is the number of years remaining on the loan

The value of A in this scenario is the semi-annual payment.

Initially, the interest rate is 0.055 and the number of years remaining is 25.

After the first 5-year period, the interest rate goes up by 12%, so is multiplied by a factor of 1.12 to become 6.16% per year. The same growth factor is applied to the interest rate at the beginning of each 5-year period.

Of course, the number of years remaining is decreased by 5 years at the beginning of the next 5-year period.

The Principal remaining at the end of each 5-year period is the starting principal for the next period. It is calculated from ...

FV = P(1 +r/2)^10 -A((1 +r/2)^10 -1)/(r/2)

Where P is the starting principal, A is the loan payment as calculated above, and r is the annual interest rate.

These formulas are built into spreadsheet functions, so the desired set of loan payments can be calculated easily by that technology. The result is attached. In the "# pmts" column is the value used to amortize the loan for the 5-year period. The semiannual payment is calculated as though the loan would be completely paid off in that number of payments, keeping the same interest rate for the duration. Of course, that payment series is interrupted and the loan recalculated at the beginning of the next 5 years.

The half-yearly payments for each 5-year interval are ...

$33,336.83

$35,176.68

$36,869.23

$38,266.75

$39,158.08

_____

<em>Additional comment</em>

The values displayed in the spreadsheet are rounded to the values shown. The values used in calculation have 14 or more significant digits. This means the numbers here may vary from those provided by a lending institution. In the real world, the principal and interest values are rounded to cents with each payment, so actual results may vary by a few cents either way.

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Help me with this please

Elenna [48]

Answer:

2,700 sq yds :)))) (d)

Step-by-step explanation:

2(30)=60

1.5(30) =45

60(45)= 2700

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3 years ago

Find the domain of the function (f/g)(x) given f (x)=x^2-4x-5 and g(x)=x^2-25

stealth61 [152]

Answer:

all real numbers except ±5.

Step-by-step explanation:

Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.

The domain of (f/g)(x) is all real numbers except ±5.

___

Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:

add 25 and take the square root: x^2=25; x=±√25.
factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.

5 0

2 years ago

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the p

KIM [24]

Answer:

<em>1885.5 m^3 of water</em>

Step-by-step explanation:

I'll assume this is the complete question

<em>Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14 </em>

<u><em>The pool forms</em></u><em> a cylinder with a radius of 12 feet and a height of 4.5 feet.</em>

height of pool = 4.5 ft

radius of pool $12^{2}$ = 12 ft

height of water is 4 inches below pool top

<em>12 inches make 1 ft</em>

4 inches = 4/12 ft = 0.33 ft

Therefore, height of water = 4.5 - 0.33 = 4.17 ft

<em>volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed</em>

volume of cylinder formed by the water = volume of water = π $r^{2}$ h

volume = 3.14 x $12^{2}$ x 4.17 = <em>1885.5 m^3 of water</em>

3 0

3 years ago

four distinct circles are drawn in a plane. what is the maximum number of points where at least two of the circles intersect?

kolezko [41]

90 points where at least two of the circles intersect.

<h3>Define circle.</h3>

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,

Four distinct circles are drawn in a plane.

Start with two circles; they can only come together in two places. The third circle contacts each of the previous two circles in two spots each, bringing the total number of intersections up to four with the addition of a third circle. The total number of intersections will rise by another 6 when a fourth circle intersects the first three. And the list goes on.

As a result, we get a recognizable, regular pattern: for each additional circle, there are two more intersections overall than in the circle before it.

The total number of intersections can be expressed as the sum because the maximum number of intersections of 10 circles must occur when each circle contacts every other circle in 2 places each.

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90.

90 points where at least two of the circles intersect.

To learn more about circle, visit:

brainly.com/question/11213974

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1 year ago

According to a survey conducted by the U.S. Department of Health and Human Services, about 50% of U.S. adults age 18 and older a

liraira [26]

Using a confidence interval, we have that:

a) The range is from 48.8% to 51.2%.

b) Between 125,000 and 131,000 adults are registered organ donors.

<h3>What is a confidence interval?</h3>

A confidence interval is given by the <u>estimate plus/minus the margin of error</u>.

For this problem, we have that:

The estimate is of 50%.

The margin of error is of 1.2%.

The bounds of the range are given as follows:

50% - 1.2% = 48.8%.

50% + 1.2% = 51.2%.

Hence the range is from 48.8% to 51.2%.

<h3>What are the total numbers?</h3>

We have to find <u>48.8% and 51.2% of 255,200,373</u>, hence:

0.488 x 255,200,373 = 124,537,782.

0.512 x 255,200,373 = 130,662,591.

Rounded to hundredth thousand, between 125,000 and 131,000 adults are registered organ donors.

More can be learned about confidence intervals at brainly.com/question/25890103

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7 0

1 year ago