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dsp73
3 years ago
9

Find the interest earned and the future value of an annuity with annual payments of $1,400 for 18 years into an account that pay

s 4% interest per year.
Mathematics
1 answer:
o-na [289]3 years ago
5 0

Answer:

interest earned= 1436.143

the future value of an annuity= 2836.143

Step-by-step explanation:

Given Data:

Interest rate= 4%

time,t = 18 years

Annual payment, P= 1400

At the end of 18 years, final investment A= ?

As per the interest formula for interest

A= P(1+r)t

Putting the values in above equation

= 1400(1+0.04)^18

= 2836.143

Interest earned = A-P

                           = 2836.143-1400

                          = 1436.143 !

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A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
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Answer:

Part A) y=\frac{3}{4}x-\frac{1}{4}  

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Part C) y=\frac{2}{7}x+\frac{8}{7}

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the  median from N

we Know that

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step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

we have

L(-3, 6) and P(1, -8)

substitute the values

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step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

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we have

N(3, 2) and M(-1,-1)

substitute the values

m=\frac{-1-2}{-1-3}

m=\frac{-3}{-4}

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Find the equation of the line in point slope form

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we have

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substitute

y-2=\frac{3}{4}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{3}{4}x-\frac{9}{4}

y=\frac{3}{4}x-\frac{9}{4}+2

y=\frac{3}{4}x-\frac{1}{4}  

Part B) Find the equation of the  right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

we have

L(-3, 6) and P(1, -8)

substitute the values

M(\frac{-3+1}{2},\frac{6-8}{2})

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step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}  

we have

L(-3, 6) and P(1, -8)

substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

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step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

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we have

m_1=-\frac{7}{2}

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m_2=\frac{2}{7}

step 4

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

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substitute

y+1=\frac{2}{7}(x+1)

step 5

Convert to slope intercept form

Isolate the variable y

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y=\frac{2}{7}x+\frac{2}{7}-1

y=\frac{2}{7}x-\frac{5}{7}

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

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Find the slope of the segment LP

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m=\frac{y2-y1}{x2-x1}  

we have

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substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

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step 2

Find the slope of the perpendicular line to segment LP

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If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

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we have

m_1=-\frac{7}{2}

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m_2=\frac{2}{7}

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

point\ N(3,2)

substitute

y-2=\frac{2}{7}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{2}{7}x-\frac{6}{7}

y=\frac{2}{7}x-\frac{6}{7}+2

y=\frac{2}{7}x+\frac{8}{7}

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