Find the doubling time of an investment earning 7% interest if interest is compounded continuously

Answers

Answer 1

Answer:

The doubling time of this investment would be 9.9 years.

Step-by-step explanation:

The appropriate equation for this compound interest is

A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.

If P doubles, then A = 2P

Thus, 2P = Pe^(0.07t)

Dividing both sides by P results in 2 = e^(0.07t)

Take the natural log of both sides:  ln 2 = 0.07t.

Then t = elapsed time = ln 2

                                       --------- = 0.69315/0.07 = 9.9

                                         0.07

The doubling time of this investment would be 9.9 years.

Answer 2

To calculate the doubling time for an investment earning 7% interest compounded continuously, the Rule of 70 is used, which suggests that the investment will double in approximately 10 years.

To find the doubling time of an investment earning 7% interest compounded continuously, we can use the Rule of 70. The Rule of 70 is a quick and useful formula that estimates the number of years it takes for an investment to double given a fixed interest rate, specifically for interest rates below 10%. Here's how you can use it:

Take the number 70 and divide it by your interest rate. In this case, the interest rate is 7%.The formula looks like this: Doubling Time (in years) = 70 / interest rate.Therefore, the doubling time for an investment earning a 7% interest rate is approximately 70 / 7, which equals 10 years.

The Rule of 70 assumes continuous compounding. Thus, if an investment has a consistent return of 7% per year, compounded continuously, it will take roughly 10 years to double.

It's also worth noting that the Rule of 72 can be used in a similar way to estimate the doubling time more roughly. In this case, using the Rule of 72, dividing 72 by the interest rate of 7% would provide an estimation of approximately 10.3 years. This is a close approximation and often used due to its simplicity.


Related Questions

Help please! 8th grade math! ASAP

Answers

17. 1lb is the better deal

18. about $17

19. 1.5lbs I think

20. 7000lbs

Write two mixed numbers where the LCD is 12, but the product of the denominators in not 12?

Answers

Step-by-step explanation:

The prime factorization of 12 is

 12 = 2²×3

To find denominators suitable for your purpose, you need to group the factors

 {1, 2, 2, 3}

into two groups with different products that share at least one of the numbers that is not 1.

For example, your grouping could be (2, [2), 3], where a 2 is shared. That is, your denominators could be 2*2=4 and 2*3=6.

Another possible grouping is (1, [2), 2, 3], giving rise to denominators of 2 and 12.

Yet another is (1, [3), 2, 2], for denominators of 3 and 12.

Using the first grouping, a pair of mixed numbers matching your requirement might be

 1 3/4, 5 1/6

Graph the system of equations {3x+y=6 -3x-4y=12

Answers

Answer:

  see attached

Step-by-step explanation:

A graphing calculator can easily show you a graph of these equations. (see attached)

__

If you want to graph them by hand, it is convenient to make use of the x- and y-intercepts. For an equation in standard form each of the intercepts is found by dividing the constant by the coefficient of the variable

  ax +by = c . . . . . . equation of a line

  x-intercept: c/a

  y-intercept: c/b

__

For the first equation, the intercepts are ...

  x-intercept: 6/3 = 2, point (2, 0)

  y-intercept: 6/1 = 6, point (0, 6)

For the second equation, the intercepts are ...

  x-intercept: 12/-3 = -4, point (-4, 0)

  y-intercept: 12/-4 = -3, point (0, -3)

In each case, the line can be drawn through the plotted intercept points.

Can someone please help thanks

Answers

Answer:

C.

Step-by-step explanation:

You have to find the area by doing b×h=a.

Brady and 3 friends went to lunch at Mazzio’s Pizza. Their meal cost $32, and they left a 15% tip. How much was the total bill, including tip?

Answers

Answer:36.80

Step-by-step explanation:

15% of 32 is 4.8 so add that

Final answer:

To find the total bill for Brady and his friends at Mazzio's Pizza, including a 15% tip on a $32 meal, you calculate the tip as $4.80. Adding the tip to the original cost gives a total bill of $36.80.

Explanation:

Brady and his friends' meal at Mazzio's Pizza cost $32, and they want to leave a 15% tip. To calculate the tip amount, convert the percentage to a decimal form by dividing by 100 (15% becomes 0.15), and then multiply by the cost of the meal.

This results in $32 × 0.15 = $4.80. With the added tip, the total bill becomes $32 (meal cost) + $4.80 (tip) = $36.80. So, the total bill including the tip is $36.80.

Learn more about Total Bill Calculation here:

https://brainly.com/question/17745127

#SPJ2

Find the equation of the line that is perpendicular to the line y = 4 and passes through the point (−2, 1).
A) x = −2
B) y = −1
C) y = 1
D) x = 2

Answers

Answer:

A

Step-by-step explanation:

y = 4 is a horizontal line parallel to the x- axis with a slope of zero

A line perpendicular to it is a vertical line parallel to the y- axis

The equation of a vertical line is x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (- 2, 1) with x- coordinate - 2, hence

x = - 2 ← equation of perpendicular line → A

Answer:

A. [tex]x=-2[/tex]

Step-by-step explanation:

We are asked to find the equation that is perpendicular to line [tex]y=4[/tex] and passes through the point [tex](-2,1)[/tex].

We can see that our given equation is a horizontal line, which crosses y-axis at point [tex](0,4)[/tex].

Every vertical line is perpendicular to a horizontal line. We know that equation of a vertical line is in form [tex]x=a[/tex], which crosses x-axis at point [tex](a,0)[/tex].

Since we need to find the equation that passes through point [tex](-2,1)[/tex], so our required equation will pass x-axis at [tex]-2[/tex].

Therefore, our required equation would be [tex]x=-2[/tex] and option A is the correct choice.

PLEASE HELP WILL GIVE POINTS PLEASE HELP PLEEEEAAAASSSSE!!!!!!!!!!!!!

Answers

Answer:

0.1 repeating

Step-by-step explanation:

To write 5/45 as a decimal you have to divide numerator by the denominator of the fraction.  

We divide now 5 by 45 what we write down as 5/45 and we get 0.11111111111111  

divide 5 by 45 to find the decimal:

5 / 45 = 0.111 ( the one keeps repeating.

When a number in a decimal is repeating you put a line over it.

The answer would be 0.1 with a line over the one, which is the 3rd answer.

Need steps for both questions

Answers

11.

6x-3y=18

-3y=-6x+18

y = (-6x +18)/-3

y = 2x - 6

12.

-3x-7y=14

-7y=3x+14

y=(-3/7)x - 2

Answer:

[tex]\large\boxed{Q10.\ y=2x-6}\\\boxed{Q12.\ y=-\dfrac{3}{7}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Q 10.

[tex]6x-3y=18[/tex]       subtract 6x from both sides

[tex]6x-6x-3y=-6x+18[/tex]

[tex]-3y=-6x+18[/tex]          divide both sides by (-3)

[tex]\dfrac{-3y}{-3}=\dfrac{-6}{-3}x+\dfrac{18}{-3}\\\\y=2x-6[/tex]

Q 12.

[tex]-3x-7y=14[/tex]            add 3x to both sides

[tex]-3x+3x-7y=3x+14[/tex]

[tex]-7y=3x+14[/tex]            divide both sides by (-7)

[tex]\dfrac{-7y}{-7}=\dfrac{3}{-7}x+\dfrac{14}{-7}\\\\y=-\dfrac{3}{7}x-2[/tex]

solve 41x-17y=99 17x-41y=75​

Answers

I got no solution....

Answer:

X= 2  Y= -1

Step-by-step explanation:

Help please i need help

Answers

I think the answer is (C)?

Answer:

C

Step-by-step explanation:

The area (A) of a circle is calculated using the formula

A = πr² ← r is the radius = 17.5

A = π × 17.5² = π × 306.25 ≈ 962 m² → C

Janet has some five dollar bills and one dollar bills in her wallet. Altogether she has 20 bills and a total of $52. How many bills dose she have

Answers

Final answer:

By setting up a system of equations and solving it, we find that Janet has 8 five dollar bills and 12 one dollar bills in her wallet.

Explanation:

The student's question requires solving a system of linear equations to find out how many of each type of bill Janet has.

To solve this problem, let's use two variables: x for the number of five dollar bills and y for the number of one dollar bills.

Janet has 20 bills in total which gives us the first equation x + y = 20.

She also has a total of $52, so the value of her five dollar bills plus the value of her one dollar bills equals 52, providing us our second equation 5x + y = 52.

To solve the system of equations, we can use substitution or elimination.

Let's use substitution by expressing y from the first equation: y = 20 - x.

Now we can substitute y in the second equation with 20 - x, which after simplification gives 5x + 20 - x = 52, and then 4x = 32.

Dividing by 4 gives us x = 8.

This means Janet has 8 five dollar bills.

Now we can substitute x back into y = 20 - x to find out y, which gives us y = 20 - 8 = 12.

So, Janet has 12 one dollar bills.

Final answer:

Janet has 8 five dollar bills and 12 one dollar bills in her wallet. This was determined by setting up a system of equations and solving for the number of $5 and $1 bills based on the given total number of bills and the total cash amount.

Explanation:

To solve the problem concerning the number of $5 and $1 bills Janet has, you can set up a system of equations. Let's indicate the number of $5 bills as f and the number of $1 bills as o. We're given two pieces of information: the total number of bills is 20, and the total amount of money is $52. This can be translated into two equations:

f + o = 20 (total number of bills)

5f + o = 52 (total amount of money in dollars)

To find out how many of each bill Janet has, subtract the first equation from the second one:

5f + o - (f + o) = 52 - 20

5f - f = 52 - 20

4f = 32

f = 32 / 4

f = 8

Janet has 8 five dollar bills. To find the number of one dollar bills, subtract 8 from the total number of bills:

o = 20 - 8

o = 12

Janet has 12 one dollar bills.

Hector made a batch of pancakes for his guests

Answers

I think it is the first.I would choose that.

Answer:

9/6 and 3/2

Step-by-step explanation:

Let's remember the definition of "constant of proportionality":

The constant of proportionality is the constant value of the ratio k of two proportional quantities x and y; usually written y = kx.

In our case, x is the cups of milk and y is the cups of pancake mix. We need to find out k.

9 = k*6

9/6 = k

If we simplified the fraction, we have 3/2 (is equivalent to 9/6).

The correct answers are 3/2 and 9/6.

At a neighborhood park, there are 11 spaces for bicycles on a rack by the basketball court. The bicycle rack by the playground has 3 times as many spaces for bicycles as the one by the basketball court. What equation can be used to find the total number of bicycles spaces on the rack by the playground?

Answers

Answer:

Since they are 11 spaces for bicylces and the playground has as many spaces for bicycles then we use this equation 3 x 11 = 33  to find the total number of bicycles spaces on the rack by the playground.

Write the point-slope equation of the line that passes through (3, -1) and a slope of 2.

Answers

Answer:

y=2x+(-7)

Step-by-step explanation:

y=2x+c

solve for c

-1=2(3)+c

-1=6+c

-6-1=c

c=-7

y=2x+(-7)

Answer:

[tex]\large\boxed{y+1=2(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the slope m = 2 and the point (3, -1). Substitute:

[tex]y-(-1)=2(x-3)\\\\y+1=2(x-3)[/tex]

**WILL MARK BRAINLIEST AND THANK YOU**

Choose all of the statements listed here that are true about the change over time as indicated by the fossil record.

Birds and flowering plants inhabited this area at about the same time period.

Animals with shells and fish appeared on Earth before land plants.

Flowering plants were critical to the appearance of insects.

Vascular plants appeared during the same period as mammals.

Humans were the last to appear at this site.

Answers

Answer:

1,2, and 5

Step-by-step explanation:

This can be determined by looking at the graph

Answer:

The correct answer would be "Animals with shells and fish appeared on earth before land plants." and "Humans were the last to appear at this site."

Step-by-step explanation:

On the graph, it shows that the land plants were a little further ahead in time from the shelled animals and the fish, And the humans were shown last, even after the plants.

PLEASE HELP I WILL GIVE BRAINLIST!

Answers

To find the unit rate divide the total miles by the total hours:

225 / 4 = 56.25 miles per hour

What is the first term when applying Binomial theorem

Answers

Answer:

1

Step-by-step explanation:

Binomial theorem is describing the expansion of powers of the term (a + b)^n

Obviously if n = 0, a + b = 1

So the first term is 1.

8.....,,,,,,,,,,,,,,,,

Answers

Answer:

option (a)

(a³-b³)^1/4

Step-by-step explanation:

Given in the question an expression

4√a³-b³

To find,

this expression without radicals

There is another way to represent the taking of a root. You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. a√x = (x)1/a

Example

√a = a^1/2

∛a = a^1/3

So, similarly the expression 4√a³-b³  =  (a³-b³)^1/4

finding the missing numbers. show the work. 26-4=12+ ?​

Answers

Answer:

? = 10

Step-by-step explanation:

26 - 4 = 12 + ?

22 = 12 + ?

10 = ?

Answer:

10

Step-by-step explanation:

Let the missing number be x.

Then,

26 - 4 = 12 + x

12 + x = 22

x + 12 - 12 = 22 - 12 ( subtract 12 from both sides to single x in LHS)

x        = 10

∴ the missing number is 10.

Hope this helped you :)

PLZ HURRY! Identify the unit rate in the graph.

Answers

20; 3g*h. Hd. So, adding in the. Variables. Then 20

Answer:B) 10$

Usatestprep

How do I show my work??

Answers

you would show the long division

Answer:

u can use long division

Step-by-step explanation:

10788 divided by 31 is 348 because

31 cant go into 1 so do it again

31 cant go into 10 so again

31 can go into 107 3 times leaving 14

add the 14 to 8 and so on

answer this FAST!
4x^2–20x+25 for x= −2

Answers

Answer:

81

Step-by-step explanation:

To evaluate substitute x = - 2 into the expression

4( - 2)² - 20(- 2) + 25

= (4 × 4) + 40 + 25 = 16 + 40 + 25 = 81

cosA + cosB + cosC = 1 + 4sinA/2 sinB/2 sinC/2

Answers

[tex] \cos(A) + \cos( B ) + \cos(C) \\ = 2 \cos( \frac{A + B}{2} ) \cos( \frac{ A- B}{2} ) + 1 - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2\cos( \frac{\pi - C}{2} ) \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}] \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A + B}{2} )] \\ = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2} +\frac{A - B}{2} }{2} ) \sin( \frac{ \frac{A + B}{2} - \frac{A - B}{2} }{2} ) \\ = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}[/tex]

What are the intercepts of y = 4x − 2?

Answers

Answer: y = −2

Step-by-step explanation:

0 = −4x − 2x = −1/2To find the y-intercept, substitute in 0 for x and solve for y. Y = − 4 * 0 −2Which then gives you y = - 2

* Hopefully this helps:) Mark me the brainliest:)

Answer:

D

Step-by-step explanation:

(0.5, 0) and (0, -2)

Out of 54 randomly chosen football players in a football league, 11 said they were going to attend camp there are 810 players in the entire league
How many players in the league would you expect to attend camp?

A 54

B 437

C 165

D 20

Answers

The ratio is 54:11
Divide 810 by 54 to see what you need to multoply by. Doing this gives you15
Now multiply 11 by 15 and you get 165. So 165 people out of 810 people are attending camp. Hope this helps

First we find the average out of the total. 11÷54=0.20 this is the percentage wanting to attend. now we times this number by the total number of football players. 810 X 0.20 equals 165. your answer is C.

Which quantity is proportional to 65⁄5? Check all that are true. 13⁄1 260⁄10 195⁄15 130⁄15 130⁄10

Answers

Answer: 13/1, 195/15, 130/10

Step-by-step explanation: The easiest way to solve this problem is to work your way though each of the options. 13/1 is the original reduced by 5, 195/5 is both multiplied by 3 and 130/15 is both multiplied by 2. The other two options do not have a way to multiply or divide them to get the original number.

Answer:

Step-by-step explanation:

65/5 is reduceable to 13/1.  So is 195/15.  So is 130/10.  All of these ratios are proportional to 13/1.

Mack bought two CDs for $14.50 each, one wallet for $12.00, and four picture frames at $7.50 each. What is the average cost of each item rounded to the nearest dollar?

Answers

Answer:

$71 dollars

Step-by-step explanation:

What you have to do is do 14.50 times 2 to get 29.

Then 7.50 times 4 to get 30.

You will then add 29+30+12=$71 dollars.

Answer:

(14.5+14.5+12+7.5+7.5+7.5+7.5 )= 71

71/7 = 10$

Please help, step by step, I need to show the work, I just don’t know how to do it

Answers

Answer:

B

Step-by-step explanation:

The volume (V) of a rectangular prism is

V = lbh

where l is the length, b the width and h the height

We are looking for 3 values that multiply together to give 10

Considering each of the options

A

100 × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 25 ≠ 10

B

10 × [tex]\frac{1}{2}[/tex] × 2 = 10

C

5 × 2[tex]\frac{1}{2}[/tex] × 2[tex]\frac{1}{2}[/tex] = 31.25 ≠ 10

D

10 × 10 × [tex]\frac{1}{2}[/tex] = 50 ≠ 10

B is the only possible dimensions for the prism

simplify: (6x^3)÷(3x+12)​

Answers

(6x^3)/(3(x+4))= 2x^3/(x+4)

name a fraction equivalent to 2/3​

Answers

Answer:

4/6, 6/9, 8/12, 10/15

A fraction that is equivalent to [tex]\frac{2}{3}[/tex] is [tex]\frac{20}{30}[/tex]

Although these fractions have different numerators and denominators, they still have the same value because they equal each other.

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