To save money for his daughter's college tuition, Pablo invests $279 every quarter in an annuity that pays 6% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 22 years. Do not round any intermediate computations, and round your final answer to the nearest cent

Answers

Answer 1

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\dotfill &279\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &22 \end{cases}[/tex]

[tex]A=279 \left[ \cfrac{\left( 1+\frac{0.06}{4} \right)^{4 \cdot 22}-1}{\frac{0.06}{4}} \right]\implies A=279\left[\cfrac{1.015^{88}~~ - ~~1}{0.015} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 50348.47~\hfill[/tex]


Related Questions

please help me answer this question.. no links​

Answers

Answer:

The answer is 28 Units

It's number 3.

5 Ed has two dogs. The smaller dog weighs
83 pounds. The larger dog weighs 13 times
as much as the smaller dog. How much does the larger dog weigh?

Answers

Answer:

1,079 more pounds

Step-by-step explanation:

because if you do 83x13 you will get 1,079

For which inequality is x = 5 a solution

Answers

Answer:

4<x<6

Step-by-step explanation:

4 is smaller than x

and x is samller than 6

so its 5

Solve for the unknown side and find perimeter of the figure below note that the figure is not drown to scale.​

Answers

Answer:

[tex]x = 12\ m,\ perimeter = 63\ m[/tex]

Step-by-step explanation:

Step 1:  Determine x

[tex]\frac{15\ m}{10\ m} = \frac{x}{8\ m}[/tex]

[tex](15\ m*8\ m) = (10\ m * x)[/tex]

[tex]120\ m^2 / 10\ m = x * 10\ m / 10\ m[/tex]

[tex]12\ m = x[/tex]

Step 2:  Determine the perimeter of the figure

[tex]18\ m + 15\ m + 10\ m + 8\ m + 12\ m[/tex]

[tex]63\ m[/tex]

Answer:  [tex]x = 12\ m,\ perimeter = 63\ m[/tex]

7x=7.7 How would i figure this out ?

Answers

Divide by 7 on both sides to get x

Expand and simplify (x - 7)(x + 4)

Answers

Answer:

x^2 - 3x - 28

Step-by-step explanation:

(x-7)(x+4) = x^2 + 4x - 7x - 28 according to the distributive property

Which = x^2 - 3x - 28

Answer:

[tex]x^{2} -3x-28[/tex]

Step-by-step explanation:

[tex](x - 7)(x + 4)\\x(x + 4)-7(x + 4)\\x^{2} +4x-7x-28\\x^{2} -3x-28[/tex]

Which table represents a linear function?
x
X
y
x
х
y
1
y
0
y
1
0
0
0
0
0
1
2
1
1
1
1
1
3
AN
low
N
4
3
2
0
N
5
2
3
3 3
8.
3
6
3
1
3
7
O
o

Answers

Answer:

  (d)  see attached

Step-by-step explanation:

A linear function has equally-spaced outputs for equally-spaced inputs. The given tables all have sequential values for x, so we can find the linear function by looking at the differences of y-values.

  a) 2 -1 ≠ 4 - 2 . . . . not linear (exponential)

  b) 1 -0 ≠ 3 -1 . . . . not linear (quadratic)

  c) 1 - 0 ≠ 0 - 1 . . . . not linear

  d) 3 -1 = 5 -3 = 7 -5 . . . . a linear function

✏Answer ✏

Letter D. A linear function.

Step-by-step explanation:

# Brainliest Bunch

Find the area of the polygon

Answers

Answer:

40

put some efforts dude...they are so easy

Answer:

40

Step-by-step explanation:

area of a triangle= ½×base× height½×4×6=10since the polygon ha four equal triangles with the same measurement,multiply by four10×4=40ans=40

hope that helps

A woman bought some large frames for ​$18 each and some small frames for ​$8 each at a closeout sale. If she bought 21 frames for ​$​248, find how many of each type she bought.

Answers

Answer:

8 large frames and 13 small frames

Step-by-step explanation:

Given:
$18 each = large frames

$8 each = small frames

To Find:

⇒  Bought 21 frames for ​$​248, find how many of each type she bought

Solve:

1 Large frame costs = 18 $

Therefore, x large frames costs = 18x $

{where x is the number of large frames she bought}

1 Small frame costs = 8 $

Therefore, x Small frames costs = 8y $

{where y is the number of small frames she bought}

By the given condition :

18x + 8y = 248        {equation 1}

x + y = 21                 {equation 2}

Solve these equations simultaneously, from second equation we get :

x = 21- y

18⋅(21−y)+8y= 248

378 - 18y+8y = 248

-10y = -130

y = 13

Put y = 13 in eq x = 21- y

x = 21  - y

x = 21 - 13

x = 8

So the woman bought 8 large frames and 13 small frames.

~lenvy~

With a choking victim, the rescuer will provide abdominal thrusts which should be performed
by:
A. None apply
B. Pressing in the person's chest with hard and fast compressions,
C. Making quick inward and upward thrusts to the abdominal cavity with your fist.
D. Lying the person on their back and pushing up into their stomach and rib cage.

Answers

the answer is C never lie the person down and you don’t press on the chest because it’s in the abdomen

5) If the mean of the following data is 20.2, find the value of p. Variable (x) 10 15 20 25 30 Frequency (fi) 6 8 p 10 6​

Answers

Answer:

p = 20

Step-by-step explanation:

Step1 :

Multiply each value by its  frequency then  add up :

(10 × 16) + (15 × 8) + (20 × p) + (25 × 10) + (30 × 6) = 20p + 610

Step2 :

Calculate the total of the frequencies :

6 + 8 + p + 10 + 6 = p + 30

The mean is equal to

[tex]\frac{20p+610}{p+30}[/tex]

Therefore

[tex]20.2 = \frac{20p+610}{p+30}[/tex]

then

20.2 × (p + 30) = 20p + 610

then

20.2p + 606 = 20p + 610

Then

20.2p -  20p = 610 - 606

Then

0.2p = 4

Then

p = 4/(0.2)

  = 20

find the term to term rule for the following sequence 2,6,18, 54, 162

Answers

*3 or multiply by 3

:)

Answer:

multiply 3 or *3 that is 2*3=6

Les gusta mi dibujo a mano con lapiz y papel

Answers

Está bonito, solo algunos detalles, pero con practica creeme que va estar mejor. Los dedos de las manos hay que trabajar más, ¡Está bonito!

Someone help me out with this!!

Answers

Answer:

Missing Angle = 75 degrees

This answer may not be correct, if it is or is not, please tell me in the comments!

Step-by-step explanation:

The Missing Angle:

All of the angles add up to 180 since it is a triangle, so the equation is:

90 (the box aka right angle) + 15 + (the missing angle) = 180

Then, add 90 + 15 = 105. After that, do:

180 - 105 = 75 degrees (don't forget the label!)

I am so sorry, but unfortunately, I do not know the answer for finding the lengths of the sides x and y.

Answer:

75°, x = 49.69, y = 12.85

Step-by-step explanation:

The missing angle is complementary with given since the triangle is right.

90° - 15° = 75°

Use trigonometry to find x

cos 15° = 48/xx = 48/cos 15°x = 49.69 (rounded)

Use Pythagorean to find y

[tex]y=\sqrt{49.69^2-48^2} =12.85[/tex] rounded

Worth 100 points IF answered correctly:

Answers

8/6 is the answer because 8 x 1/6 is 4/3 and 8/6 = 4/3

Answer:

8/6

Step-by-step explanation:

Sam has 8 times the number of eggs Kyle has can be expressed as:

[tex]\displaystyle \large{8\cdot \dfrac{1}{6}}[/tex]

As given, the number of eggs Kyle has is 1/6 so out of 6 eggs, Kyle only had 1.

Therefore, 8 multiplies/times the number of eggs is:

8/6

Write an equation in slope-intercept form of the line shown.
An equation is

Answers

Answer:

y = 3/4x - 1

Step-by-step explanation:

m = (1-4)/(4-8) = -3/-4 = 3/4

b = (0, -1)

y = mx + b

y = 3/4x - 1

BRAINLIEST please if this helps!
Y=3/4x -1
-1 is the lines y-intercept
And from (4,1) to (8,4) it goes up 3 and to the right 4

You are a teller at a bank. A customer has $252 in their checking account. They write a check for $287 (debit) that is cashed by the recipient . Will the new balance be positive or negative?

Answers

Negative. You have $252, and the check will take away $287, so 252-287 is -35.

What's the difference between arithmetic and geometrical sequence with examples please.​

Answers

Answer:

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

-- Credit -- libretexts

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Answer:

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

Step-by-step explanation:

solve it in form of cos and sin pls​

Answers

[tex]\text{L.H.S}\\\\=\dfrac{\cot A}{1- \tan A} + \dfrac{\tan A}{1- \cot A}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{1- \tfrac{\sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{1-\tfrac{\cos A}{\sin A}}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{\tfrac{\cos A- \sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{\tfrac{\sin A - \cos A}{\sin A}}\\\\\\=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} + \dfrac{\sin^2 A}{\cos A(\sin A - \cos A)}\\\\\\[/tex]

[tex]=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} - \dfrac{\sin^2 A}{\cos A(\cos A - \cos A)}\\\\\\=\dfrac 1{\cos A - \sin A} \left( \dfrac{\cos^2 A}{\sin A} - \dfrac{\sin^2 A}{\cos A}\right)\\\\\\=\dfrac 1{\cos A - \sin A} \left(\dfrac{\cos^3 A - \sin^3 A}{\sin A \cos A} \right)\\\\\\=\dfrac 1{\cos A - \sin A} \left[\dfrac{(\cos A - \sin A)(\cos^2 A + \sin^2 A + \sin A \cos A)}{\sin A \cos A} \right]\\\\\\=\dfrac{\cos^2 A + \sin^2 A+\sin A \cos A}{\sin A \cos A}\\\\\\[/tex]

[tex]=\dfrac{\cos^2 A}{\sin A \cos A}+\dfrac{\sin^2 A}{\sin A \cos A}+\dfrac{\sin A \cos A}{\sin A \cos A}\\\\\\=\dfrac{\cos A}{\sin A} + \dfrac{\sin A}{\cos A} + 1\\\\\\=\cot A + \tan A + 1\\\\\\=1 + \tan A + \cot A\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Bame has a bag of $1 and $2 coins
The total mase of the coins is 71.4 grams
Bame knows that
• the mass ofa$1 coin is 9 grams and
* the mass of a $2 coin is 6.6 grams
What is the value of the coins in a bag

Answers

Answer:

$13

Step-by-step explanation:

9x + 6.6y = 71.4

6.6(4) = 26.4

71.4 - 26.4 = 45

9 / 45 = 5

$2 = 4

$1 = 5

$2 * 4 = $8

$1 * 5 = $5

$8 + $5 = $13

Don’t even know to be honest

A case of soda has 12 cans. Each can holds 360 milliliters of soda. What is the total
number of liters of soda in the case?

Answers

Answer:

4.32 Liters

Step-by-step explanation:

12*360 mL= 4320 mL

mL to L= mL/1000

4320/1000= 4.32

Find the slope of the line (2,-3) (4,-7)

Answers

hello!

Use the slope formula:-

[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]

[tex]\displaystyle\frac{-7-(-3)}{4-2} =\frac{-7+3}{2} =\frac{-4}{2} =\bigstar{\boxed{\pmb{-2}}}[/tex]

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

can somebody help me im confused

solve the equation

Answers

Check the picture below.

the assumption is that the graph keeps on going all the way to ±infinity.

Bear in mind that the interval notation is referring to the endpoints on the x-axis.

In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three more then the sum of the other digits. Find the three digits if the sum of all three digits is 15. Then find the number.

Answers

Answer:

591

Step-by-step explanation:

Let's use algebra to solve this question:

Units digit = x

Hundreds digit = x+4

Tens digit = 3 + (x+4) + x = 2x +7

All 3 digits = 15

so x + (x+4) + 2x + 7 = 15

4x +11 =15

4x = 4

x = 1

Then you substitute:

Units = 1

Hundreds = 1+4 = 5

Tens = 2(1) + 7 = 2 + 7 = 9

The number is therefore 591.

Donte bought a computer that was 20% off the regular price $1,080. If an 8% sales tax was added to the cost of the computer, what was the total price donte paid for

Answers

Answer:

$933.12

Step-by-step explanation:

So 20% of $1,080 is 216.

1080 - 216 is 864

8% of 864 is 69.12

864 + 69.12 would be $933.12

(x^2 - 14x + 48) divided (x-6)

Answers

Answer: (x^2 - 14x + 48) : (x-6) = 0(x^2 - 14•x + 48) : (x-6) = 0x = 8

Step-by-step explanation:

i hope this is the answer your looking for

please help.. no links​

Answers

Answer:

Its 9.0 units

Step-by-step explanation:

For the side mostly to the left, its gonna be 3 units, since we can easlily count it

Now, for the diagonals, we have to use the formula for the area of a triangle, which is (l * w) / 2 = a.

For the bottom side, its 3 along the x axis and 1 along the y axis. 3 * 1 is 3, now divide that by 2 and you got 1.5

Now, for the right side, its 5 on the y, 1 on the x. Multiply 1 by 5, you got 5. Now divide that by 2 and you have 2.5

Finally, for the top side, its 4 on the x, and 1 on the y. 4 * 1 is 4, divided by 2 and its 2.

Alright, now we have to add 'em all together. 3 + 1.5 + 2.5 + 2 is 9 units

Theres your answer :)

Select the correct answer.
The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?



A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6

Answers

Answer:

That would be week 2 and 4 (B). They are both at 12 students attending

20 characters just for you brainly

Answers

Answer:

first and last option

Step-by-step explanation:

the first and the last are increasing from left to right since the slope is positive.

A credit card had an APR of 25.67% all of last year and compounded interest daily. What was the credit card's effective interest rate last year?

a
28.25%
b
29.25%
c
28.92%
d
27.32%

Answers

Answer:

The answer is 29.25%.

Step-by-step explanation:

I think it is B
Hope this is right!!!
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