If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?

A. $30.72

B. $41.12

C. $46.52

D. $53.76

Answers

Answer 1

[tex]\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$3000\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=years\to &4 \end{cases} \\\\\\ A=3000(1+0.05\cdot 4)\implies \boxed{A=3600}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3000\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases}[/tex]

[tex]\bf A=3000\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=3000(1.05)^4\implies \boxed{A=3646.51875}\\\\ -------------------------------\\\\ \stackrel{\textit{compounded interest}}{3646.51875}~~-~~\stackrel{\textit{simple interest}}{3600}[/tex]

Related Questions

The area of a square garden is 98 meters squared. How long is the diagonal

Answers

Because it is square that means its equal on all sides 98 meters

No se jaja yo también tengo tarea que hacer

This number represents the number of times the base is used as a factor

Answers

It is the exponent.

The exponent is the number used in a power to represent the number of times the base is used as a power.

For example: 7^2. The number 2 is the exponent and it indicates that the number 7 (which is the base) is used two times as a factor, this is, 7^2 = 7 * 7.

Othe example: 4^6. The exponent 6 indicates that the base 4 is used 6 times as a factor => 4^6 = 4 * 4 * 4 * 4 * 4 * 4.

is (3,13) a solution of the equation y=4x

Answers

y=4x
13 = 4(3)
13 = 12 ...not true

answer
(3,13) is not a solution of the equation y=4x

No because 13 = 4(3) is not equal. So the answer is no.

What is "The sum of m and n"

Answers

3x-x+2=4...this is your answer to this question

m + n, pretty sure since there is no known number for n nor m so you would write it like this. So you would put m + n equals a number. Me and my science partner have carefully dissected this problem.

What is the probability that the selected consumer is 35–55 years old or likes crunchicles?

Answers

Final answer:

The probability that a selected consumer is 35–55 years old or likes crunchicles is 0.5.

Explanation:

To determine the probability that the selected consumer is 35–55 years old or likes crunchicles, we need to add the probabilities of these two events happening individually and subtract the probability of both events happening. Let's assume the probability of a randomly selected consumer being 35–55 years old is 0.4 and the probability of a randomly selected consumer liking crunchicles is 0.3. The probability of a randomly selected consumer being both 35–55 years old and liking crunchicles is 0.2. Therefore, the probability that the selected consumer is 35–55 years old or likes crunchicles is:

P(35-55 or crunchicles) = P(35-55) + P(crunchicles) - P(35-55 and crunchicles)

= 0.4 + 0.3 - 0.2 = 0.5

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ12

If a production line produces 50 mouse traps every 30 minutes over the course of a 10-hour work day with a half hour break for lunch how many mouse traps are made in a day

Answers

950 mouse traps

100 traps/ 1 hr times 9.5 hrs = 950

50 mouse traps every 30 minutes.....double that and u get 100 mouse traps per hr.

10 hrs - half hr break (30 minutes) = 9.5 hrs of work

so if it is 100 mousetraps per hr...and the hrs worked are 9.5 hrs.....then the number of mousetraps produced are : 9.5 * 100 = 950 mouse traps <==

an air traffic controller is tracking two planes. To start, playing a is at an altitude of 2814 ft and plan B is just taking off. Plan a is gaining altitude at 30.5 feet per second in playing day is gaining altitude at 80.75 feet per second. How many seconds will pass before the planes are on the same altitude

Answers

Model the altitude of each plane with a linear equation.
The initial altitude is the 'y-intercept'.
The rate of elevation is the slope.

Plane A: y = 30.5x + 2814

Plane B: y = 80.75x

The planes will be at same altitude when the y values are equal.
80.75x = 30.5x + 2814

Solve equation for 'x'.
80.75x - 30.5x = 2814
50.25x = 2814
x = (2814/50.25) = 56

Answer:
It will take 56 seconds before planes are at same altitude.

Answer:

56 seconds will pass.

Step-by-step explanation:

Because its right. :)

please give brainliest

Mike has $880 in his savings account and adds $24 per week. at the same time, leslie has $520 in his savings account and adds $36.00 per week. how long will it take leslie to have the same amount as mike?

Answers

30 weeks

880+24x=mike
520+36x=leslie

880+24x = 520+36x

360=12x
x=30 weeks

A bank offers a money market account paying 4.9% interest compounded semiannually. A competing bank offers a money market account paying 4.8% interest compounded daily. Which account is the better investment?

Answers

Assume $1000 at 4.9% semi-annually = $1,049.60
Assume $1000 at 4.8% daily = $1,049.17

Let's try a bigger number $50'000 4.9% semi-annually $52,480.01
$50,000 4.8% daily = $52,458.37
It's a wash, the question is how long will you be investing, that might make a difference. I calculated 12 Millions over 6 years and bank A would be the better choice. Semi-annual compounded at 4.9%

what two consecutive numbers the square root of 10 between

Answers

[tex]\bf \sqrt{10}\approx 3.162278 \\\\\\ \boxed{3}\text{\textemdash\textemdash\textemdash}3.162278\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{4}[/tex]

the table shows the low temperature in five cities on a winter day. which statement is true

A. it is warmer in Tacoma than in Roseville

B. it is colder in Roseville Than in Helena

C. It is warmer in Helena than in Fargo

D. it is colder in Tacoma than in Great Falls

Answers

The answer to that question so D because 1.0 is the lowest tem.

Suppose a and b are 3x3 matrices, with det(a) = 5 and det(b) = 3.
a. det(2a) = ? 4 pts
b. det((ab)-1) = ?

Answers

[tex]\det(2\mathbf A)=2^3\det\mathbf A=8\times5=40[/tex]

[tex]\det(\mathbf{AB})^{-1}=\dfrac1{\det\mathbf{AB}}=\dfrac1{\det\mathbf A\det\mathbf B}=\dfrac1{5\times3}=\dfrac1{15}[/tex]

Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.

Splash of Color will always charge the least.

If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.

If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.

If it takes 3 hours to paint the rooms, both companies will charge the same amount.

Answers

Answer:

The correct statements are 1, 3, and 5.

Explanation:

Let's calculate the total cost for each company based on the given information:

For Interior Designs USA:

- Evaluation fee: $60.00

- Labor cost per hour: $35.00

- Total labor cost for 7 hours: $35.00/hour × 7 hours = $245.00

- Total cost = Evaluation fee + Total labor cost = $60.00 + $245.00 = $305.00

For Splash of Color:

- Labor cost per hour: $55.00

- Total labor cost for 7 hours: $55.00/hour × 7 hours = $385.00

Now, let's analyze the statements:

1. If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. - True. ($305.00 < $385.00)

2. Splash of Color will always charge the least. - False. In this case, Interior Designs USA charges less for 7 hours of work.

3. If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. - True. As we've seen, Splash of Color charges $55.00 per hour, while Interior Designs USA charges $35.00 per hour plus an initial fee.

4. If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. - False. Let's calculate:

- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 10 hours = $60.00 + $350.00 = $410.00

- Splash of Color: $55.00/hour × 10 hours = $550.00

Splash of Color charges $550.00 - $410.00 = $140.00 more, not $200. Therefore, this statement is false.

5. If it takes 3 hours to paint the rooms, both companies will charge the same amount. - False. Let's calculate:

- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 3 hours = $60.00 + $105.00 = $165.00

- Splash of Color: $55.00/hour × 3 hours = $165.00

They both charge $165.00, so this statement is true.

So, the correct statements are 1, 3, and 5.

A flea weighs 8 decigrams, and an ant weighs 3 milligrams. How much more does a flea weigh than an ant?

Answers

now, a decigram is "deci" one tenth of a gram, 1/10 gram.

whilst a milligram is "milli" one thousandth of a gram, 1/1000 gram

now, the flea is 8 of those decigrams thus is 8 * (1/10) grams

the ant is 3 of those milligrams thus 3 * (1/1000) grams

let's find their difference.

[tex]\bf 8\left( \frac{1}{10} \right)\implies \cfrac{8}{10}\implies \stackrel{decigrams}{\cfrac{4}{5}} \\\\\\ 3\left( \frac{1}{1000} \right)\implies \stackrel{milligrams}{\cfrac{3}{1000}}\\\\ -------------------------------\\\\ \cfrac{4}{5}-\cfrac{3}{1000}\impliedby \textit{our LCD is 1000}\implies \cfrac{(200\cdot 4)-3}{1000}\implies \cfrac{800-3}{1000} \\\\\\ \cfrac{797}{1000}\implies 797\left( \frac{1}{1000} \right)\implies 797~milligrams[/tex]

Answer:

797 milligrams

Step-by-step explanation:

Hope this helps!

rachel's necklace cost 20% more than Tammy's shoes. Bryan' s video game cost 30% more than Rachel's necklace. If Tammy's shoes cost $30.00, what did Brian's video game cost?

Answers

I believe Brian's game would be $46.80
30*20%=6
30+6=36
36*30%=10.80
36+10.80=46.80
hope this helps!

Answer:

46.80

Step-by-step explanation:

Pls brainly I need it so bad I spent 10 minutes of my time to solve this.

In a steel titanium alloy, 360 grams of steel were required to make 1200 grams of the alloy. How much titanium was required to make 1600 grams of the alloy?

Answers

check mathematics app

Consider the graph of f(x)=1/x. Which functions result in a vertical compression? Check all that apply.
a. g(x)=1/3x
b. g(x)=3/x
c. g(x)= - 3/x
d. g(x)= - 1/3x

Answers

I believe the answer would either be a or b.

Hope this helps!

Answer:

A & D

Step-by-step explanation:

What's the range of 37000 and 45000

Answers

Range: Subtract 37000 from 45000 and you'll have it.

The mailman delivered a $22 check and 3 - $14 bills today. He also took back 1- $5 bill. What is the total in the mailbox?

Answers

3 Times 14 is 42
42+22 is 64
64-5= 59

Solve P=2D+2C for D

Answers

P-2c/2 = D So, P-2c all over 2 is equal to D.

Answer: D = (P - 2C)/2

Step-by-step explanation:

We want to solve P= 2D + 2C for D

This means "isolate D in one side of the equation"

The first step is subtracting 2C in the both sides of the equation:

P - 2C = 2D + 2C - 2C = 2D

P - 2C = 2D

Now, we want to take of the multiplication that is acting on D, so we divide in both sides by 2:

(P - 2C)/2 = (2D)/2 = D

Now we have D isolated, and this is:

D = (P - 2C)/2

The domain for f(x) and g(x) is the set of all real numbers. let f(x) = 3x + 5 and g(x) = x2. find g(x) − f(x). x2 − 3x − 5 3x3 − 5x2 3x2 − 5 x3 − 5

Answers

f (x)=3x+5
g (x)=x^2

g (x)-f (x)=(x^2)-(3x+5)
=x^2-3x-5

What number is 49 less than 78

Answers

If you want to subtract the answer is -29.

The number that is 49 less than 78 is 29.

jackson made 15 calls in 20 minutes. how many calls per minute did he make

Answers

i think it's .75...:')

Hello User :)

How are you doing?
In this case, your trying to find how many calls he makes per minute. So here we go! We know he made 15 calls in 20 minutes! Therefore, we must divide to find the unit number, which basically is "Numbers Simplified."

[tex]15 / 20=0.75[/tex]

That means he makes 0.75th of a call in 1 minute.

A miner descended 1500 feet into a mine. While in the mine, he then rose 1200 feet and then descended 850 feet. What was the miner's net gain or loss in altitude?

Answers

Call descending a negative number and rising a positive number.
Then add the numbers.

A miner descended 1500 feet into a mine.
-1500 ft

he then rose 1200 feet
+1200 ft

then descended 850 feet
-850 ft

Now add the three numbers:
-1500 ft + 1200 ft + (- 850 ft) = -1150 ft

Since the sum is a negative number, that means
he had a net loss in altitude of 1150 ft.

If there were a million cars in line, bumper to bumper, with a average length of 10.14 feet, how long would that line be in miles? (Round to the nearest mile)

Answers

The answer is 10,140,000fett because 10.14(the length of each car) times 1,000,000 is 10,140,000

1,920 miles long

Hope this helps : )

Find the roc of the volume of a cube with respect to the length of its side s

Answers

If the length of one side of a cube is s, then the derivative of the formula for the volume of the cube is

dV/ds = 3s^2.

The roc of the volume of a cube with respect to the length of its side s is 3s².

What is rate of change?

The rate of change of a function is the rate at which the output values change over the input value.

The rate of change of a function is one degree less than the actual function.

The volume of a cube is :

V = s³

The rate of change of volume V with respect to length a will be :

dV/ds = d(s³ )/ds

= 3s²

This means that, a cubic function will have a quadratic rate of change

Hence, The roc of the volume of a cube with respect to the length of its side s is 3s².

Answers

336 is kaylas number, hope this helps

633 is the number

6 is the hundreds place
3 is the number that is 3 less than the hundreds number (6)
6+3=9
12-9=3
3 is your last digit

i hope you understood

Harrison mows lawns and rakes leaves for his summer and fall weekend jobs. He gets $10 an hour to mow lawns and $8 an hour to rake leaves. If, during September, Harrison mows for m hours and rakes for 12 hours, which expression represents the amount of money he makes? Harrison mows lawns for 11 hours, so m = 11. How much money does he make in September?

Answers

total money= 10m+8(12)

Answer:

first one is 10m+8(12)

second one is 206

Step-by-step explanation:

i took it alrr..

Which equation has the same solution as 4-2(x-5)-x-19

Answers

i believe the equation with the same solution is -3x-5

The equation 3x - 4 = 2x + 7 has the same solution as 4 - 2(x - 5) = x - 19, with both solutions yielding x = 11.

Let's solve the equation step-by-step: 4 - 2(x - 5) = x - 19

First, expand the left side:
4 - 2x + 10 = x - 19Combine like terms:
14 - 2x = x - 19Move all terms involving x to one side:
14 = 3x - 19Move constant terms to the other side:
33 = 3xSolve for x:
x = 11

Now, let's compare this solution to other given equations:

2(x + 5) = -8
2x + 10 = -8
2x = -18
x = -9 (Not a match)3(x - 3) = 9
3x - 9 = 9
3x = 18
x = 6 (Not a match)x + 2 = 2x - 3
2 = x - 3
x = 5 (Not a match)3x - 4 = 2x + 7
3x - 2x = 7 + 4
x = 11 (Match)

The equation with the same solution as 4 - 2(x - 5) = x - 19 is 3x - 4 = 2x + 7.

Complete question: Which equation has the same solution as 4 - 2(x - 5) = x - 19?

2(x + 5) = -83(x - 3) = 9x + 2 = 2x - 33x - 4 = 2x + 7

Tim bought a pen for $2.25, a pencil for $0.59, a notebook for $6.49, and a highlighter for $1.49. He used a coupon that gave him $5.25 off his entire purchase. How much did he spend in total?

Answers

Add together the prices: $10.82. This is reduced by the value of the coupon: 10.82-5.25=$5.57.

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If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest? A. $30.72 B. $41.12 C. $46.52 D. $53.76

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If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?

A. $30.72

B. $41.12

C. $46.52

D. $53.76