Ask question

Ask question

All categories

nikitadnepr [17]

2 years ago

10

Bob and Kathy want to save a total of $500,000 for retirement. How much should they deposit monthly into an account that pays 3.

9% interest,
compounded monthly, to meet their goal in 24 years?
$1,051.17
$2,102.34
$950.41
$4,446.41

1 answer:

kifflom [539]2 years ago

6 0

Answer:

it would 4,446.41

Step-by-step explanation:

You might be interested in

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

2 years ago

1) Given the formula for the general term of an arithmetic sequence, determine t12.

o-na [289]

It’s B hope this helps

8 0

3 years ago

What is 352+525261 :D

sergey [27]

The correct answer is "525613"

6 0

2 years ago

What is 3/18 written in simplest form explain how you found your answer

GaryK [48]

1/6 because 3 goes into 3 once, and 3 goes into 18 6 times. So the fraction is 1/6

7 0

2 years ago

Read 2 more answers

What is 5/20 simplified ?

andre [41]

5/20 simplified is 1/10

it's simple math

5 0

2 years ago

Read 2 more answers