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raketka [301]
2 years ago
12

Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselv

es the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 7.5%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old.
How much money will they have to have saved by the time they are 60 in order to reach their retirement goal?

If they do live the full 30 years, and spend their full quarterly budget, how much money in total will they have lived on/spent in their retirement?

How much will have been earned in interest?

If they saved the same total amount of their own money, but no interest earned over the years whatsoever, how much would be available to live on each quarter?
Mathematics
1 answer:
GuDViN [60]2 years ago
8 0

Answer:

5

Step-by-step explanation:

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Given the data points, (x, y) of a linear function: (2, 11), (4, 10), (6, 9), (12, 6), what is the function? What is the slope?
NeX [460]

Answer:

The function is y~=~12 ~-~ 0.5 \cdot x.

The slope is m=-0.5.

The y-intercept is b=12.

Step-by-step explanation:

Our aim is to calculate the values <em>m</em> (slope) and <em>b</em> (y-intercept) in the equation of a line :

y=mx+b

We have the following data:

\begin{array}{c|cccc}x&2&4&6&12\\y&11&10&9&6\end{array}

To find the line of best fit for the points given, you must:

Step 1: Find X\cdot Yand X\cdot X as it was done in the table below.

Step 2: Find the sum of every column:

\sum{X} = 24 ~,~ \sum{Y} = 36 ~,~ \sum{X \cdot Y} = 188 ~,~ \sum{X^2} = 200

Step 3: Use the following equations to find <em>b</em> and <em>m</em>:

\begin{aligned}        b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 36 \cdot 200 - 24 \cdot 188}{ 4 \cdot 200 - 24^2} \approx 12 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 4 \cdot 188 - 24 \cdot 36 }{ 4 \cdot 200 - \left( 24 \right)^2} \approx -0.5\end{aligned}

Step 4: Assemble the equation of a line

\begin{aligned} y~&=~b ~+~ m \cdot x \\y~&=~12 ~-~ 0.5 \cdot x\end{aligned}

The graph of the regression line is:

5 0
3 years ago
If 3x = y - 5 and x = -4, then y = ? <br> A)-7 <br> B)3 <br> C)7 <br> D)17 <br> E)9
fredd [130]

Answer:

<h3>3×(-4) = y - 5</h3><h3>= ) -12 = y -5 </h3><h3>=) -12 +5 =y </h3><h3>=) -7 = y</h3>

<h2>y =-7</h2>

8 0
3 years ago
Read 2 more answers
Please help asap 20 pts
kherson [118]

It is associative property

8 0
3 years ago
HELP DUE AT MIDNIGHT TN
White raven [17]

Answer:

102

Step-by-step explanation:

These angles are congruent due to corresponding angles thm

3x + 21 = 6x - 60

3x - 6x = -60 - 21

-3x = -81

x = 27

3x + 21

3(27) + 21

81 + 21

102

8 0
2 years ago
In the xy-plane, the equations x + 2 = 10 y and 3 +6 = x y c represent the same line for some constant c. What is the value of c
aalyn [17]

Answer:

C=30

Step-by-step explanation:

Supposing that we have the lines

x+2=10y

and

3x+6=Yc.

Note that dividing by 3 the second line can be rewritten as

x + 2= Y c/3.  

Remember that a line is written as ax+b=dY, in our case, both lines have a=1 and b=2. Therefore, in orther that the two lines are equal, we need that 10=c/3, hence c=30.

3 0
3 years ago
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