Amelia is going to invest in an account paying an interest rate of 2.3% compounded quarterly. How much would Amelia need to invest, to the nearest hundred dollars, for the value of the account to reach $1,530 in 19 years?

Answers

Answer 1

Answer:

Amelia needs to invest $989.57.

Step-by-step explanation:

The compound interest formula is given by:

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Amelia is going to invest in an account paying an interest rate of 2.3% compounded quarterly.

This means that \(r = 0.023, n = 4\).

How much would Amelia need to invest, to the nearest hundred dollars, for the value of the account to reach $1,530 in 19 years?

We have to find P for which \(A(t) = 1530\) when \(t = 19\). So

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

\(1530 = P(1 + \frac{0.023}{4})^{4*19}\)

\(P = \frac{1530}{(1 + \frac{0.023}{4})^{4*19}}\)

\(P = 989.57\)

Amelia needs to invest $989.57.


Related Questions

Ten boxes of paper weigh 260 pounds. Mrs. Thomas
ordered 24 boxes of paper for the science department.
How many pounds do 24 boxes of paper weigh?

Answers

Answer:

624 pounds

Step-by-step explanation:

If 10 boxes of paper weigh 260 pounds, one box of paper is equal to 26 pounds because 260 divided by 10 is equal to 26. If one box equals 26 pounds, 24 boxes times 26 pounds each is equal to 624 pounds.

Help help help help help help help help help help help

Help help help help help help help help help help help

Answers

Answer:

A' 2,2

B' 3, -1

C' -1,0

Step-by-step explanation:

Because you're translating it by -2, 3, you're basically subtracting 2 from the x value and adding 3 to the y value.

A = 4, -1

A' = 2, 2

B = 5, -4

B' = 3, -1

C = 1, -3

C' = -1, 0

9
LBCA and LACD form a linear pair. LBCA is
represented by (2x - 5)° and LACD is
represented by (3x + 10)°.
What is the mLACD?
A. 35°
B. 61°
C. 65°
D. 115°

9LBCA and LACD form a linear pair. LBCA isrepresented by (2x - 5) and LACD isrepresented by (3x + 10).What

Answers

Answer:

D

Step-by-step explanation:

\(m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}\)

Katrina walked 3 and 7/10 miles on Monday and 2 and 5/10 miles on Wednesday. How many miles did she walk in all?

Answers

Answer:

Hello

Step-by-step explanation:

The answer is 6 1/2

Houses cover 51% of the area of a desert community. Use the grid to model the community and complete the statements. The entire area of the community is represented by squares. The squares that have houses on them represent the area of the community covered with houses.

Answers

Answer:

Too lazy To type put here is an image

Houses cover 51% of the area of a desert community. Use the grid to model the community and complete

Answer:

The entire area of the community is represented by  

   49

   51

✔ 100

   151

squares.

The  

   49

✔ 51

   100

   151

squares that have houses on them represent the area of the community covered with houses.

If a0=10 and an+1=-5an then find the value of a4

Answers

The value of a4 would be equal to -666.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that \(a_0=10\) and \(a_n+1=-5a_n\)

This is a recursive formula. So we can simply substitute in each value. For instance, a₂

Use the recursive definition repeatedly.

a2 = -5(6) +4 = -26

 a3 = -5(-26) +4 = 134

 a4 = -5(134) +4 = -666

Therefore, the value of a4 is -666

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2051
20
SINO-V3 COSO - 2
2​

Answers

Answer:WHAT DOES THAT EVEN MEAN!?!?

Step-by-step explanation:

!!!!!!!!

Each of the counting problems below can be solved with stars and bars. For each, say what outcome the diagram
∗∗∗|∗||∗∗|
represents, if there are the correct number of stars and bars for the problem. Otherwise, say why the diagram does not represent any outcome, and what a correct diagram would look like.

a.) How many ways are there to select a handful of 6 jellybeans from a jar that contains 5 different flavors?
b.) How many ways can you distribute 5 identical lollipops to 6 kids?
c.) How many 6-letter words can you make using the 5 vowels in alphabetical order?
d.) How many solutions are there to the equation. show bars and stars.
x1+x2+x3+x4=6.

Answers

Hello! This question is hard to answer because at some parts it cut the text off. Are you able to post a picture of the question?

James invested some money at 6% interest. James also invested $211 more than 4 times that amount at 11%. How much is invested at each rate if James receives $1522.21 in interest after one year?

Answers

$1,488.45 is invested at 6% and $6,164.8. is invested at 11%.

What is Interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

James invested some money at 6% interest.

James also invested $211 more than 4 times that amount at 11%.

Let x represent the amount invested at 6%.

Then (4x+211) is the amount invested at 11%.

So, The total interest earned in 1 year is

(11%)(x) +(16%)(4x+211) = 1561.50

0.11x + 0.16(4x+ 211)= 1522.21

0.11x + 0.64x + 33.76 = 1522. 21

0.75 x = 1,488.45

x= 1,488.45

 

and, 4x +211 = 4(1488.45) + 211 = $6,164.8.

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Los 1600 euros de alquiler de un terreno se reparten entre tres ganaderos que llevan alli a pastar sus ovejas. Como no tienen el mismo número de ovejas, deciden pagar proporcionalmente al número de ovejas de cada uno. Si el primero tiene 120 Ovejas,el segundo 72 y el tercero 68. ¿ Cuánto paga cada uno?

Answers

So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

What is proportion?

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

A rectangular board is 1.5 meters long and 1.2 meters wide. What is the area of the board in square millimeters?

Answers

1 meter = 1000mm

Convert the dimensions to mm:

1.5 x 1000 = 1500 mm

1.2 x1000 = 1200 mm

Area = length x width

Area = 1500 x 1200 = 1,800,000 square mm

Whats the correct answer answer asap for brainlist

Whats the correct answer answer asap for brainlist

Answers

Answer:

A) The verb "waddled" most accurately and vividly describes the action in this situation, as "waddle" is a verb used to describe a slow and awkward gait often associated with a heavily pregnant woman. This verb conveys the idea of the woman's awkward and unsteady movement, making it the most accurate and vivid description of her actions.

i need help really bad

i need help really bad

Answers

Answer:

see explanation

Step-by-step explanation:

If f(x) and \(f^{-1}\) are inverse functions, then

f(\(f^{-1}\))(x) = x

Thus substitute x = \(f^{-1}\) (x) into f(x)

f(\(\frac{x+6}{5}\) )

= 5 (\(\frac{x+6}{5}\) ) - 6

= x + 6 - 6

= x

Thus f(x) and \(f^{-1}\) (x) are inverse functions

Which is true about investments and risk?

Answers

Answer:

Every investment carries some degree of risk, All investments carry some degree of risk. Stocks, bonds, mutual funds, and exchange-traded funds can lose value, even all their value, if market conditions sour. Even conservative, insured investments, such as certificates of deposit (CDs) issued by a bank or credit union, come with inflation risk. They may not earn enough over time to keep pace with the increasing cost of living.

Step-by-step explanation:

A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
A. 9
B. 4/3
C. 1/4
D. 3/4
Please select the best answer from the choices provided.

Answers

It’s answer D
8+3+1=12
1-3/12=3/4

HELLO PLEASE HELP Add using a number line.


​−34+114​


Drag and drop the word SUM to the correct value on the number line. WHOEVER ANSWERS GETS BRAINEST!!

Answers

Answer:

The answer is 80

Step-by-step explanation: You can trust me ok?:)

Answer:

The arrow should point at 0.5 which is half way between 0 and 1

Step-by-step explanation:

- + 1 = -3/4 + 5/4 = 2/4 = 1/2 and 1/5 in decimal form is 0.5

pls brainliest:)d

Johanna rode her bike 7 miles to a lake . She rode 3/4 of the distance to the lake before lunch

Answers

Answer:

The answer would be 5.25 miles :)

What I did was I took 3/4 and made it into its decimal form which is 3/4. I then times it by 7 to get 5.25.
5.25 miles is your answer.

I was wondering if anyone knew how to solve this

I was wondering if anyone knew how to solve this

Answers

Answer:

2

Step-by-step explanation:

Nina can stitch of a dress in 4 hours. If d represents the number of dresses and h represents the number of hours, which equation represents this proportional relationship?

Answers

According to mathematics it’s 6 hours because the force and the matter is 6 minutes away from 7 hours

Answer:d=6h

trust bro its right

ANSWER QUICK PLS WILL MARK BRAINLIEST
You should spend no more than 30% of your take-home pay on rent. Your take-home pay is $1,625 per month. How much
can you afford to pay for rent per month? (Remember to have a $ and 2 decimal places in your answer)

Answers

Answer: $487.50

Steps:
1,625 * 0.30 = 487.5
$487.50

30% of your take-home pay (1,625) is $487.50

if a pound of almonds cost eight dollars how many ounces can be bought for $3.80

Answers

Proportions

A pound of almonds is said to cost 8 dollars.

But one pound is equivalent to 16 ounces, therefore:

16 ounces cost 8 dollars

Dividing by 8 we get that

2 ounces of almonds cost 1 dollar

Thus, for $3.80 we can buy 2*3.80 = 7.60 ounces of almonds

The function B is defined by the equation B(x)=10x+25
Find the value of each expression:
B(6)=
B(2.75)=
B(1.482)=

Solve each equation:
B(x)=93; x=
B(x)=42.1; x=
B(x)=116.25; x=

Answers

10(6) + 25 = 60 + 25 = 85

10(2.75) + 25 = 27.5 + 25 = 52.5

10(1.482) + 25 = 14.82 + 25 = 39.82

93 = 10x + 25 || 68 = 10x || x = 6.8

42.1 = 10x + 25 || 17.1 = 10x || x = 1.71

116.25 = 10x + 25 || 91.25 = 10x || x = 9.125

The value of each expression is given below,

B(6)=85

B(2.75)=52.5

B(1.482)=39.82

Value of x for each expression,

B(x)=93; x=6.8

B(x)=42.1; x=1.7

B(x)=116.25; x=9.125

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is B(x)=10x+25.

The value of each expression will b calculated as,

10(6) + 25 = 60 + 25 = 85

10(2.75) + 25 = 27.5 + 25 = 52.5

10(1.482) + 25 = 14.82 + 25 = 39.82

93 = 10x + 25 || 68 = 10x || x = 6.8

42.1 = 10x + 25 || 17.1 = 10x || x = 1.71

116.25 = 10x + 25 || 91.25 = 10x || x = 9.125

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If -3x–7 =23 then 6x=?

Answers

Answer:

6x = -60

Step-by-step explanation:

-3x - 7 = 23

-3x = 30

x = -10

6(-10) = -60

²-6x +10 is to be written in the form (x-p)² +g. Find the values of p and q.​

Answers

Answer:

\(p = 3\\\\q= 1\)

Step-by-step explanation:

\(x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1\)

A group of cyclists recorded the distance they have traveled.
Draw a line plot and answer the questions below.
Name
Gina
Rey
Faye
Mark
John
James
Albert
William
Nathan
Kate
Mary
Risa
Paul
Abi
Joan
Distance in
miles
40 1/2
50
35 3/4
60
45
55 1/4
60
45
40 1/2
50
45
40 1/2
60
40 1/2
35 3/4
Title:
1. How many cyclists were there?
2. What was the longest distance traveled?
3. How many cyclists traveled less than 50 miles?
4. What was the most common distance traveled by
the cyclists?
5. How many more cyclists traveled 45 miles than
55 1/4 miles?
6. How many cyclists traveled more than 45 miles

Answers

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Use Demoivres Theorem to find (-square root 3 +i)^6

Use Demoivres Theorem to find (-square root 3 +i)^6

Answers

Answer:

\(z=(-\sqrt{3}+i)^6\) = -64

Step-by-step explanation:

You have the following complex number:

\(z=(-\sqrt{3}+i)^6\)       (1)

The Demoivres theorem stables the following:

\(z^n=r^n(cos(n\theta)+i sin(n\theta))\)      (2)

In this case you have n=6

In order to use the theorem you first find r and θ, as follow:

\(r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°\)

Next, you replace these values into the equation (2) with n=6:

\(z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64\)

Then, the solution is -64

Answer:

A) -64

Step-by-step explanation:

Edge 2021

Use Demoivres Theorem to find (-square root 3 +i)^6

Susan is running a 5k race. The graph of distance vs. time is shown.
What interval is she running the fastest?

Susan is running a 5k race. The graph of distance vs. time is shown.What interval is she running the

Answers

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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Order the side lengths EF, FG, and GE from least to greatest,
(Note that the figure is not drawn to scale.)
A
44

Order the side lengths EF, FG, and GE from least to greatest,(Note that the figure is not drawn to scale.)A44

Answers

Answer:

Angle g=76 degrees

the order i would say is EF,GE,FG

tell what you get

You're welcome

Step-by-step explanation:

Triangle equal 180 degrees so 180-60-44=76

so last angle is 76 degrees

Three specimens of Alloys A, B, C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in the alloy A?

Answers

Answer:

X=10%

Y=30%

Step-by-step explanation:

The required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Percentage of copper in A = 1/2 [percentage of copper in ingot]
                                         = 1/2 × 20% = 10%

Percentage of zinc in A = 1/3 [percentage of zincin ingot]
                                    = 1/3 × 40% = 13.34%

Thus, the required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

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The question seems to be incomplete,
Complete question.
Three specimens of Alloys A, B, and C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in alloy A when copper is half of the copper in the ingot and zinc is 1/3 of the zinc in the ingot?

need help with This Math ​

need help with This Math

Answers

The number of intersection points is (a) 1 point or 2 points.

How to determine the number of intersection points

Given that

Line AB and circle P lie on the same plane.

And, we have

AP = 6 mm

BP = 8 mm

The intersection points can be 0, 1, or 2.

Since the radius of circle P is 6mm, any intersection point must also be 6mm away from P.

Next, we have the following test cases

If line AB intersects circle P at one point, then that point must be on the circle centered at P and have a radius of 6mm. If line AB intersects circle P at two points, then both points must be on the same circle centered at P with a radius of 6mm.

Hence, the answer is (A) 1 point or 2 points.

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