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Use the formula A = P( 1 + r/n)^(nt) to calculate the balance A of an investment (in dollars) when P = $4000, r = 4%, and t= 10years, and compunding is done by the day, by the hour, by the minute, and by the second. (Round your answers to the nearest cent).

a. compounding by the day: A= $

b. compounding by the hour: A= $

c. compounding by the minute: A= $

d. compounding by the second: A= $


Does increasing the number of compoundings per year result in unlimited growth of the balance? yes or no (choose one)

Answers

Answer 1

Answer:

a. compounding by the day: A = $5967.17

b. compounding by the hour: A = $5967.29

c. compounding by the minute: A = $5967.30

d. compounding by the second: A = $5967.30

Step-by-step explanation:

     

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Part (a)

If the interest is compounding by the day then n = 365.

Given:

P = $4000r = 4% = 0.04n = 365t = 10 years                  

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{365}\right)^{365 \times 10}[/tex]

[tex]\implies A=4000\left(1.00010958...\right)^{3650}[/tex]

[tex]\implies A=4000(1.49179200...)[/tex]

[tex]\implies A=5967.16801...[/tex]

[tex]\implies A=\$5967.17[/tex]

Part (b)

If the interest is compounding by the hour then:

n = 365 × 24 = 8760

Given:

P = $4000r = 4% = 0.04n = 8760t = 10 years                  

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{8760}\right)^{8760 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000456...\right)^{87600}[/tex]

[tex]\implies A=4000\left(1.49182333...\right)[/tex]

[tex]\implies A=5967.29333...[/tex]

[tex]\implies A=\$5967.29[/tex]

Part (c)

If the interest is compounding by the minute then:

n = 365 × 24 × 60 = 525600

Given:

P = $4000r = 4% = 0.04n = 525600t = 10 years          

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{525600}\right)^{525600 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000007...\right)^{5256000}[/tex]

[tex]\implies A=4000(1.49182466...)[/tex]

[tex]\implies A=5967.29867...[/tex]

[tex]\implies A=\$5967.30[/tex]

Part (d)

If the interest is compounding by the second then:

n = 365 × 24 × 60 × 60 = 31536000

Given:

P = $4000r = 4% = 0.04n = 31536000t = 10 years                  

Substitute the values into the compound interest formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.04}{31536000}\right)^{31536000 \times 10}[/tex]

[tex]\implies A=4000\left(1.00000000...\right)^{315360000}[/tex]

[tex]\implies A=4000\left(1.49182390...\right)[/tex]

[tex]\implies A=5967.29562...[/tex]

[tex]\implies A=\$5967.30[/tex]

The more compounding periods throughout the year, the higher the future value of the investment.  However, the difference between compounding by the day and compounding by the second results in a difference of 13 cents over the year, which is negligible comparatively.


Related Questions

Please help take a look at this photo will give Brainly

Answers

Answer:

60 degrees

Step-by-step explanation:

On the diagram, we can see that the two angles have a dash on each of them. This means that they have the same measure.

So, if angle ABD is 60 degrees, then angle DBC would also be 60 degrees.

I hope this helps!

The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. Assuming that the population standard deviation is 3217kWh, is there sufficient evidence to support the power company's claim at the 0.02 level of significance

Answers

Answer:

The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.

Step-by-step explanation:

The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year.

This means that the null hypothesis is:

[tex]H_0: \mu = 10941[/tex]

A local power company believes that residents in their area use more electricity on average than EIA's reported average.

This means that the alternate hypothesis is:

[tex]H_a: \mu > 10941[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

10941 is tested at the null hypothesis:

This means that [tex]\mu = 10941[/tex]

To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. The population standard deviation is of 3217kWh:

This means that [tex]n = 115, X = 11425, \sigma = 3217[/tex]

Value of the z-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{11425 - 10941}{\frac{3217}{\sqrt{115}}}[/tex]

[tex]z = 1.61[/tex]

Pvalue of the test:

Probability of finding a mean above 11425, which is 1 subtracted by the pvalue of z = 1.61.

Looking at the z-table, z = 1.61 has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.

Please help me my head hurt

Answers

The answer would be A because it’s the kilometers times the amount of days to equal 30

Answer:

my head hurts also

Step-by-step explanation:

Emily wants to find out if the carpool line around her school causes too much traffic on neighborhood roads. Which is a valid sample for her survey?

Answers

Answer:

25 families living near the school

Step-by-step explanation:

Answer:

25 families living near the school :D

Step-by-step explanation:

Find the surface area of a triangle prisms

Answers

Answer: 544 sq. inch

Step-by-step explanation:

12 x 8 x 0.5 x 2 + 10 x 14 x 2 + 12 x 14 = 544

Surface of triangle = 98
x 2
= 196

10x14= 140
x3
= 420

420 + 196 = 616 inches

a triathlon event in which participants run,bike, and swim certain distances is mapped out in a triangle as shown below.

Answers

Answer:

A

Step-by-step explanation:

The statement 'the bike distance is greater than the run distance.' must be true.

The correct answer is option D.

What is distance?

"It is the length of the line joining the two points."

Angle properties:

In any triangle,

the smallest side and smallest angle are opposite one another. the mid-sized side and mid-sized angle are opposite one another.the largest side and largest angle are opposite one another.

For given example,

We have given two angles of triangle.

65° and 57°

We know, the sum of all angles of triangle is 180°.

Let 'x' be the remaining angle.

⇒ x + 65° + 57 = 180°

⇒ x +122° = 180°

⇒ x = 58°

We know,

In any triangle,

- the smallest side and smallest angle are opposite one another.

- the mid-sized side and mid-sized angle are opposite one another.

- the largest side and largest angle are opposite one another.

Here,

57° < 58° < 65°

⇒ Run < Bike < Swim

This means, the statement 'the bike distance is greater than the run distance.' is correct.

The correct answer is option D.

Learn more about angle here:

https://brainly.com/question/8729556

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ALGEBRA

tell whether the given value is a solution of the equation. (yes or no)

1. x+16=20;x+4

2. p-4+28;p+32

3. 4w+44;w=10

4. y/6= 6;y=24

Answers

Step-by-step explanation:

1. yes 4+16 = 20

2. yes 32 - 4 = 28

3. yes 4(10) = 40

4. no 24/6 = 4

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

1.yes

2.yes

3.yes

4.no

least common denominator for these two rational expressions, 3/y and
1/7y

Answers

Answer:

least common denominator = 7y

Step-by-step explanation:

3/y = 21/7y

1/7y and 21/7y have a least common denominator of 7y.

Please hurry! Timed! What is the scale factor in the dilation?
A. 2/5
B. 1/2
C. 2
D. 2 1/2

Answers

C. 2

Hope this helps!

2. Name the numerator and the denominator in each fraction.
a.
11/12
b. 7512
C.
12/0
d. 978

Answers

Answer:

a. N=11

D=12

b. N=1

D=7512

c. N=12

D=0

d. N= 1

D=978

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Answers

Answer:

The answer is The First One, IaI > b

Step-by-step explanation:

Find the zeros of the function: p(x)=(x−1)(x^2−2x−2).

Answers

Answer:

x = 6, x = -4

Step-by-step explanation:

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Answers

Answer: (0,4) and (0,0)

(Hope this helps.)

how did snidely spellbinder write a four latter word that begins and ends with e answers

Answers

Answer:

He wrote the word "ease"

Pls Help will give brainliest

2) The angle measures and/or side lengths of a triangle are described. Determine whether the conditions given determine a unique triangle (one triangle), determine more than one triangle, or cannot make a triangle. Explain how you know this.

a) 3 in., 6 in., 10 in.





b) 40°, 65°, 75

Answers

The answer is a hope this helps :) :)

Solve for f(-3)

f(x)=5-x

f(-3)= ?
pls helpppp

Answers

f(-3) = 8

Plug -3 into x and just solve it.

Given the frequency table what percentage of the students in grade 11-12 like rock music round to the nearest whole percent

Rap rock country row total
Grades 9-10. 40. 30. 55. 125
Grades 11-12. 60. 25. 35. 120
Column totals. 100. 55. 90. 245

A 10%
B. 21%
C. 25%
D 45%

Answers

9514 1404 393

Answer:

  B.  21%

Step-by-step explanation:

The number of students in grade 11-12 is given in the total column: 120.

The number of those who like rock music is given in the second column: 25.

Then the percentage in 11-12 grade who like rock music is ...

  25/120 × 100% ≈ 20.833% ≈ 21%

Write the equation of the line in fully simplified slope-intercept form.

Answers

ANSWER: y=4/3x-7

Reasoning: slope is 4/3 (change in y over change in x)
The y intercept is a -7
Then you just fill in the equation

⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️HELP HELP HELP HELP HELP HELP HELP - A right triangle has a leg length of 21 inches and a hypotenuse length of 29 inches. What is the length of the other leg? *

Answers

Answer:

[tex]20[/tex]

Step-by-step-Explanation:

Remember, the Pythagorean Theorem.

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex]21^{2} + b^{2}=29^{2}[/tex]

[tex]29^{2} -21^{2} =400[/tex]

sq rt of [tex]400=20[/tex]

Suppose that a random sample of ​twenty-year-old men is selected from a population and that these​ men's height and weight are recorded. A regression of weight on height yields ​, where Weight is measured in pounds and Height is measured in inches. What is the​ regressions weight prediction for someone who is inches​ tall

Answers

Answer:

Hello your question is incomplete attached below is the complete question

answer : 192.15 pounds

Step-by-step explanation:

Given :

weight =  - 99.41 + 3.94*Height

R^2 = 0.81

SER = 10.2

Determine the regression weight prediction

Height of man = 74 inches

Hence : weight = - 99.41 + 3.94 * 74 = 192.15

therefore the regression weight prediction = 192.15 pounds

Shshshehehehhshehesjhshshahagaga

Answers

shaheoplebqlalcjsoqldk

Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the national 40-hour average. Use the information below to calculate the t-statisic. Be sure to also specify the degrees of freedom. Weekly Hours Worked by Men Range 60 Minimum value 5 Maximum value 65 Mean 42.31 Standard deviation 10.00 Number of observations 29

Answers

Answer:

Step-by-step explanation:

The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).

HELP PLEASEEEEEE IM BEGGING YOUUU (question): Linda is making a line plot of the data below.

11.25, 12.5, 11.25, 14.125, 10.5, 11.25, 12

Which line plot represents the data correctly?

A.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
B.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 2 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
C.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 13.75 has 1 dot.
D.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 14.125 has 1 dot. ( PLEASE ANSWER ASAP) (i already made this question once pls dont get it wrong again) ill give 60 if correct!!

Answers

The answer is D ...........

Answer:

the answer is Actually A believe me i did the test

Step-by-step explanation:

A store sells 12 cans of soup for ​$21. How much would it cost you to buy 5 cans of ​soup?

Answers

Answer:

8.75$

Step-by-step explanation:

if 12 cans cost $21

1 can cost $21÷12=1.75$

5 cans = 1.75$ ×5

If a whole pan of brownies is being sold for $16, how much it cost to purchase 3/4
of the pan?

Answers

Answer:

$12

Step-by-step explanation:

We have to do this operation:

(16/4) x 3 = 4 x 3 = $12

Answer:

It will cost $12 to purchase 3/4 of the pan of brownies

Step-by-step explanation:

3/4 of 16 is equal to 12.

Hope this helps! Pls mark brainliest

Approximately how many gallons are in
7 liters? (1 L -0.26 gal.)
A 1.8 gal
C 7.3 gal
B 6.7 gal
D 46 gal

Answers

Answer:

A po ang answer kahit icompute pa po.

Step-by-step explanation:

hope it helps you po!

A bottle contains 750mL of fruit punch with a concentration of 50% pure fruit juice. Johan
drinks 100mL of the punch and then refills the bottle with an equal amount of a cheaper
brand of punch. If the concentration of juice in the bottle is now reduce to 48%, what was
the concentration in the punch that Johan added?​

Answers

Answer:

The juice concentration in the punch that Johan added was 35%.

Step-by-step explanation:

Since a bottle contains 750mL of fruit punch with a concentration of 50% pure fruit juice, and Johan drinks 100mL of the punch and then refills the bottle with an equal amount of a cheaper brand of punch, if the concentration of juice in the bottle is now reduced to 48%, to determine what was the concentration in the punch that Johan added, the following calculation must be performed:

750 = 100

650 = X

650 x 100/750 = X

65000/750 = X

86,666 = X

86.666 x 0.5 + 13.333 x 0.4 = 0.486662

86.666 x 0.5 + 13.333 x 0.39 = 0.4853287

86.666 x 0.5 + 13.333 x 0.35 = 0.4799955

Thus, the juice concentration in the punch that Johan added was 35%.

Rewrite 2/5 and 4/11 so that they have a common denominator

Answers

Answer:

22/55 and 20/55

Step-by-step explanation:

multiply 2 and 5 by 11 to get 22/55, and multiply 4 and 11 by 5 to get 20/55

For questions 1 - 4, which right triangle congruence theorem can be used to show that the two triangles
are congruent?
8
1.
2.
܂
A
B
3.
܂
4.
A

Answers

Step-by-step explanation:

1. SAS

2. HL

3. AAS

4 AAS

Mrs. Sleet said he was skinny as a rail and it looked like he hadn’t been ___
right. She gave
him his first pair of _____

please fill in the blank this is from buddy not buddy chapter 11 :)
please help

Answers

Answer:

fed,  slippers

Step-by-step explanation:

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