Jackson invested $4,200 in an account paying an interest rate of 9 1/2 compounded continuously. Julia invested $4,200 in an account paying an interest rate of 8 7/8 compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Julia's money to double than for Jackson's money to double?
Answers
It would Julia 0.60 years more to double the initial investment.
What is future value?
Future value means the initial investment multiplied by 2 since the future value is meant to double.
The formula for future value of a continuously interest rate is provided below:
FV=PV*e^(rt)
FV=future value=$4,200*2=$8,400
PV=initial investment=$4,200
e=exponential constant=2.7182818
r=interest rate=9.5%
t=number of years it takes for the investment to double=unknown
$8,400=$4,200*2.7182818^(9.5%*t)
$8,400/$4,200=2.7182818^(0.095t)
2=2.7182818^0.095t
take log of both sides
ln(2)=0.095t* ln(2.7182818)
0.095t=ln(2)/ln(2.7182818)
0.095t=0.69314718781684800
t=0.69314718781684800/0.095
t=7.30 years
The future value when interest is compounded quarterly is shown thus:
FV=PV*(1+r/4)^(N*4)
FV=$8,400
PV=$4,200
r=8 7/8%
r=8.875%
N=the number of years it would take for the initial investment to double=unknown
$8,400=$4,200*(1+8.875%/4)^(N4)
$8,400=$4,200*(1+0.0221875)^(N4)
$8,400/$4,200=(1+0.0221875)^(N4)
2=(1+0.0221875)^(N4)
2=(1.0221875)^(N4)
take log of both sides
ln(2)=N4*ln(1.0221875)
N4=ln(2)/ln(1.0221875)
N4=31.5857423180125
N=31.5857423180125/4
N=7.90
Difference in years=7.90-7.30
difference in years=0.60 years
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Related Questions
At a football stadium, 4% of the fans in attendance were teenagers. If there were 260 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
solution
4%=260
100%=?
=(100x260)/4
=6500
Percentage of fans in the stadium who were teenagers = 4%
Number of teenagers in the match = 260
Let the total number of people at the stadium be x.
Which means :
[tex] =\tt 4\% \: \: of \: \: x = 260[/tex]
[tex] =\tt \frac{4}{100} \times x = 260[/tex]
[tex] =\tt \frac{4 \times x}{100} = 260 [/tex]
[tex] = \tt \frac{4x}{100} = 260[/tex]
[tex] = \tt4x = 260 \times 100 \\ \tt \: \: \: = 26000[/tex]
[tex] =\tt x = \frac{26000}{4} [/tex]
[tex]\color{plum} =\tt x = 6500[/tex]
▪︎Therefore, number of people at the stadium = 6500
Question 6
A triangle has vertices at (-9,2).(-9, -6), and (-3,-6). What is the perimeter of the triangle in units?
Answers
Answer:
Step-by-step explanation:
Geometry plz someone help me out
Answers
Answer:
x = 7 times the square root of 3
y = 14
Step-by-step explanation:
Can removing two outliers not have an effect on the mean? Justify your responses.
Answers
H E L P ! !
The cover of a memo book must have an area of 115 cm^2. Approximately, to the nearest tenth of a centimeter, how long should each side be to make a square cover?
Answers
Answer:
10.7cm
Step-by-step explanation:
x^2= 115
x = √115
x = 10.7
Find the equation of the line
Use exact numbers
Answers
Sub in 0 to find the y intercept, and count rise over run to find the slope (1)
Answer:
y = 1x + -5
Step-by-step explanation:
slope-intercept form is y = mx + b, where m = slope and b = y-intercept.
the line touches the y-axis at -5, therefore the y-intercept, or b, is -5.
y = mx + b ⇒ y = mx - 5
now i'll find the slope by picking two points from the line and finding the change in y over the change in x, aka [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. i'll use the points (8, 3) and (5, 0) from the line in order to calculate the slope. (8, 3) can be my [tex]x_2[/tex] and [tex]y_2[/tex] and (5, 0) can be my [tex]x_1[/tex] and [tex]y_1[/tex].
first, i'm going to plug in my [tex]y_2[/tex] and [tex]y_1[/tex] values, which are the y-values from each of the coordinate pairs. since i picked (8, 3) for [tex]x_2[/tex] and [tex]y_2[/tex] and (5, 0) for [tex]x_1[/tex] and [tex]y_1[/tex], i will be plugging in 3 for [tex]y_2[/tex] and 0 for [tex]y_1[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{3-0}{x_2-x_1}[/tex]
then i'll plug in my [tex]x_2[/tex] and [tex]x_1[/tex] values, which will be 8 and 5.
[tex]\frac{3-0}{x_2-x_1}[/tex] ⇒ [tex]\frac{3-0}{8-5}[/tex]
now simplify by subtracting 0 from 3 and 5 from 8.
3 - 0 = 38 - 5 = 3the slope is [tex]\frac{3}{3}[/tex], which simplifies to 1 because [tex]\frac{3}{3}[/tex] or 3 ÷ 3 = 1.
the slope-intercept form equation for this line is y = 1x + -5 (or just y = x - 5, but since it's a fill-in-the-blank problem, the 1 will show in front of the y and -5 will come after the + sign.)
i hope this helps! have a lovely day <3
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
y = -x
Step-by-step explanation:
Let the equation representing the table attached is,
y = mx + b
Here, m = Slope of the line
b = y-intercept
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table attached,
Slope of the line passing through (23, -23) and (33, -33),
m = [tex]\frac{-33+23}{33-23}[/tex]
m = -1
Equation of the line will be,
y = -x + b
Since, this line passes through another point (43, -43),
-43 = -43 + b
b = 0
Therefore, equation of the line representing the table will be,
y = -x
ANSWER ASAP I WILL GIVE BRAINLIST
Answers
Answer:
its upside down
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
4. It takes 2 minutes to boil a single
egg. How many minutes will it take
to boil 5 eggs?
a. 10
b. 4
c. 2
d. 5
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{\#4). It takes 2 MINUTES to boil a SINGLE egg. How MANY minutes}\\\large\text{ to boil 5 eggs?}[/tex]
[tex]\large\text{\bf{Keyterm(s)}}\downarrow\\\large\text{\bf{2 minutes to boil ONE egg}}\\\large\text{\bf{Number of minutes it will take to boil FIVE eggs}}[/tex]
[tex]\textsf{Well, if one egg takes approximately two minutes, then we have we have to}\\\textsf{MULTIPLY 2 from 5, to find out your answer!}[/tex]
[tex]\large\text{\bf{2(5)}}\\\large\text{\bf{2 minutes * 5 eggs = 10 minutes to boil FIVE eggs}}\\\boxed{\boxed{\large\text{\bf{Answer: A. 10}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Evaluate the quotient of 1.05 x 103 and 1 x 103
Answers
Answer:
for the 1st one it is 108.15x
and the 2nd it is 103x
Step-by-step explanation:
The capacity of a container is 2,060 mil liters convert this to liters
Answers
Answer:
2,060 ml ÷ 1,000 = 2.06 liters
Step-by-step explanation:
1 4/5 divided by 2 7/10
Answers
Answer:
2/3Step-by-step explanation:
In order to divide fractions, you'll have to multiply the first number by the second number's reciprocal.
So it would be 1 4/5 times the reciprocal of 2 7/10.
Reciprocal of 2 7/10 = Reciprocal of 27/10 = 10/27.
So 1 4/5 x 10/27 = 2/3
Answer:
2/3
Step-by-step explanation:
1 4/5 ÷ 2 7/10
Convert these into improper fractions
(Denomintaor × whole number + numerator)/denoninator
(5 × 1 + 4)/5
9/5
(10 × 2 + 7)/10
27/10
Now the equation says:
9/5 ÷ 27/10
Use the method copy dot flip, meaning rewrite the first fraction, change the division sign to multiplication, and use the reciprocal of the last fraction
9/5 × 10/27
Multiply the numerators and denominators separately
(9 × 10)/(5 × 27)
90/135
Simplify
Both 90 and 135 can evenly fit 15
90 ÷ 15 = 6
135 ÷ 15 = 9
6/9
This can still be simplified further
Both 6 and 9 can evenly fit 3
6 ÷ 3 = 2
9 ÷ 3 = 3
2/3
This cannot be simplified any further
If 4 out of 21 people prefer diet soda to regular soda, about how many regular sodas should be bought to serve 864 people, if each person
receives one soda?
Answers
~700 regular sodas to server 864 people
(the actual answer is 699.4285)
The number of regular sodas that should be bought will be 700 regular sodas.
If out of 21 people prefer diet soda to regular soda, then it means that 17 people prefer regular soda.
Since the number of people are 864 people, then the number of regular sodas that'll be bought will be:
= 17/21 × 864
= 699.42
= 700 Approximately
Therefore, the number of regular sodas that should be bought will be 700 regular sodas.
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A newborn turtle has a shell with a 1-inch diameter. The shell keeps a similar shape as the turtle grows. After a year, the shell is 3 inches in diameter. Note: you do not need to know the shape of the shell to complete this question.
1. How many times greater is the volume of the turtle's shell after a year than it was when it was born?
2. How many times greater is the surface area of the turtle's shell after a year than it was when it was born?
Answers
Answer:
I think the volume would be 9 times greater, and the surface area would be 3 times greater
Step-by-step explanation:
Answer:
the volume would be 9 times greater
the surface area would be 3 times greater
Step-by-step explanation:
Because if the shell grows from 1 inch diameter to 3 inch diameter, the surface area will increase 3x more. And the volume I assume is 3x greater because of the height is presumably 3 inches as well.
What is the place value of 6
Answers
Answer:
6 is in ten place and its place value is 60,
Darryl is buying apples and bananas. He bought a pounds of apples that cost $2 per pound and b pounds of bananas that cost $1 per pound. The total amount of his purchase is given by the expression 2a + b. Select the terms of the expression. Mark all that apply. A 2a B 2 C A. D. B. E. 1b
Answers
Answer:
Step-by-step explanation:
I’m late lol
Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178 more cans than Shane.
write an inequality to determine the number of cans that Shane could have collected
Answers
Answer:
x+178x=2000 cans
Step-by-step explanation:
Hope this Helped
Which of the following is the equation for the line of symmetry in this figure?
Help please
Answers
Answer:
Y=-2
Step-by-step explanation:
-2y is right in between the figure.
Hope this helps!
How do I simplify 2275/6
Answers
Answer:
This fraction is at its most simplified form
Step-by-step explanation:
You can see this because the GCF of both of these numbers is 1.
The simplified form of fraction 2275/6 is 379.
We have,
To simplify the fraction 2275/6, we can divide the numerator (2275) by the denominator (6) to obtain the simplified form.
By performing the division operation, we obtained the decimal value 379.166666..., which we then rounded to the nearest whole number, resulting in 379.
This process of dividing the numerator by the denominator is the fundamental concept used to simplify fractions.
Dividing 2275 by 6:
2275 ÷ 6 = 379.166666...
Rounded to the nearest whole number, the result is 379.
Therefore,
The simplified form of fraction 2275/6 is 379.
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I need help with graphing
Answers
Ok I can help you with graphing
PLsssss I have this due in 10 minutes!!!!
Stress and strain causes rock layers to fold. The process of folding is illustrated in the diagrams below.
Which of the following correctly uses the Law of Superposition to compare the rock layers in diagram C?
Diagram C shows that layer P is above layer R and is the youngest layer.
Diagram C shows that layer P is below layer Q and remains the oldest layer.
Diagram C shows that layers P through T are in the same order as in diagram A.
Diagram C shows that layers Q through T are on the surface and are all the same age.
Answers
Answer: D
Step-by-step explanation:
The difference of 8 and 2 times m
Answers
This data gives the average number of hours different students spend on the computer each day.
Average time (hours): 1.6, 2.0, 2.0, 2.0, 1.8, 1.8, 1.5, 2.0, 1.9, 1.6, 1.9, 1.7, 1.6, 1.6, 2.0, 1.8, 1.5, 2.0
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Answers
Answer:
2 on 15, 4 on 16, 1 on 17, 3 on 18, 1 on 19 5 on 20
Step-by-step explanation:
I took the test <>_<>
HELP PLEASE! giving brainliest What would be the slope of a line parallel to the line below
Answers
-3\2 I think
Sally is flying a kite at an angle of 41 degrees. If the kite is 10 feet up in the air, how
long is the kite string?
Answers
Answer:
15.24feet
Step-by-step explanation:
Using the method of SOH CAH TOA;
Length of the kite is the hypotenuse = x
If the kite is 10 feet up in the air, then the height = 10feet (opposite)
Angle of elevation = 41 degrees
Sin theta = Opposite/hypotenuse
Sin 41 = 10/x
x = 10/sin41
x = 10/0.6561
x = 15.24 feet
Hence the kite is 15.24feet long
3x^2 + 4x -8 = 0 How many solutions will there be?
Answers
Answer:
Step-by-step explanation:
Find the average rate of change please
Answers
Answer:
The Average rate of change of function f(x)
A(x) = 3
Step-by-step explanation:
Step(i):-
Given function f(x) = x²-2
Given values x = a = -1 and x = b =4
The Average rate of change of function f(x)
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given function f(x) = x²-2
f(a) =f(-1) = (-1)²-2 = 1-2 = -1
f(b) = f(4) = (4)²-2 = 16-2 = 14
Step(ii):-
The Average rate of change of function f(x)
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
[tex]A(x) = \frac{14-(-1)}{4-(-1)} = \frac{14+1}{4+1} = \frac{15}{5} =3[/tex]
Final answer:-
The Average rate of change of function f(x)
A(x) = 3
a probability experiment consists of fair eight sided die find the probability of rolling number greater than 4
Answers
Answer:
Probability[Number greater than 4] = 1/2
Step-by-step explanation:
Given:
Total side of die = 8
Find:
Probability[Number greater than 4]
Computation:
Number greater than 4;
[5,6,7,8]
Total number greater than 4 = 4
Probability[Number greater than 4] = Total number greater than 4 / Total side of die
Probability[Number greater than 4] = 4 / 8
Probability[Number greater than 4] = 1/2
For a certain strain of bacteria, k is 0.683 when t is measured in days. Using the formula y = aek, how long will it take 12 bacteria to increase to 732 bacteria?.
Answers
Answer:
5.9 miliseconds
Step-by-step explanation:
it is it because there is a second to millisecond on a watch
40% of x is 35.
Write an equation that shows the relationship of 40%, x, and 35.
Use your equation to find x. Show your reasoning.
i really need help
Answers
So, 35/.4 is 87.5.
X= 87.5
And to change a percentage into decimals, move the . two places to the right. So, 40.0 is .4