Answer:
she can put it in a bank to gain interest
she can invest in the stock market
she can loan out money
Step-by-step explanation:
Depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
Leah's inheritance presents her with a golden opportunity to grow her wealth through strategic investment. With $12,000 at her disposal, she can explore various avenues to maximize the value of her funds. One option she's considering is investing in an account that offers a 4.5% annual interest rate.
To evaluate the potential returns from this investment, she needs to understand how different compounding frequencies affect the growth of her investment over time.
Let's start by defining the equations for the amount A(t) in the account after t years, using continuous compounding, daily compounding, and monthly compounding.
1. Continuous Compounding:
The formula for continuous compounding is given by:
[tex]\[ A(t) = P \times e^{rt} \][/tex]
where:
- A(t) is the amount of money in the account after t years,
- P is the principal amount (initial investment),
- r is the annual interest rate (expressed as a decimal),
- t is the time in years, and
- e is the base of the natural logarithm, approximately equal to 2.71828.
Using Leah's values:
P = $12,000
r = 0.045 (4.5% expressed as a decimal)
Substituting these values into the formula, we get:
[tex]\[ A(t) = 12000 \times e^{0.045t} \][/tex]
To find the amount after 10 years, we can plug t = 10 into the equation and calculate the result.
[tex]\[ A(10) = 12000 \times e^{0.045 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times e^{0.45} \][/tex]
[tex]\[ A(10) \approx 12000 \times 1.57029 \][/tex]
[tex]\[ A(10) \approx \$18,843.48 \][/tex]
So, after 10 years of continuous compounding, Leah's investment would be approximately $18,843.48.
Next, let's consider daily compounding. In this case, interest is compounded 365 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{365}\right)^{365t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{365}\right)^{365 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{365}\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00012328767123\right)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00012328767123)^{3650} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.60100220887) \][/tex]
[tex]\[ A(10) \approx \$19,212.03 \][/tex]
After 10 years of daily compounding, Leah's investment would be approximately $19,212.03.
Finally, let's explore monthly compounding. With monthly compounding, interest is compounded 12 times per year, so the formula becomes:
[tex]\[ A(t) = P \times \left(1 + \frac{r}{12}\right)^{12t} \][/tex]
Using the same values as before, we can calculate:
[tex]\[ A(10) = 12000 \times \left(1 + \frac{0.045}{12}\right)^{12 \times 10} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + \frac{0.045}{12}\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times \left(1 + 0.00375\right)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.00375)^{120} \][/tex]
[tex]\[ A(10) \approx 12000 \times (1.5722520173) \][/tex]
[tex]\[ A(10) \approx \$18,867.02 \][/tex]
After 10 years of monthly compounding, Leah's investment would be approximately $18,867.02.
In summary, depending on the compounding frequency, Leah's investment of $12,000 with a 4.5% annual interest rate would yield the following amounts after 10 years:
- Continuous compounding: approximately $18,843.48
- Daily compounding: approximately $19,212.03
- Monthly compounding: approximately $18,867.02
These calculations illustrate how different compounding frequencies can affect the growth of an investment over time. Daily compounding typically results in slightly higher returns compared to monthly compounding, while continuous compounding offers the highest potential returns due to its continuous nature.
By understanding these dynamics, Leah can make an informed decision about how to maximize the growth of her inheritance based on her investment preferences and goals.
The complete question is:
Leah has just inherited $12,000. She wants to invest the money so that she can increase the value of her inheritance. What are some of the ways she can do this?
1. Leah wants to invest the $12,000 in an account that pays 4.5% annual interest.
a. Write equations for the amount A(t) that will be in the account after t years, if the interest is
compounded continuously, daily, and monthly. Then, find the amount after 10 years, rounded
to the nearest cent, for each method of compounding.
How do you do congruent angles
Answer:
Angles are congruent if they have the same angle measure in degrees.
a meter is one thousandth of a kilometer. write an equation to show the relationship between 7 meters and 0.007 kilometer.
Need steps
Answer:
1000k=m
Step-by-step explanation:
if there is 1 meter for every 1000 kilometers, then .007 times 1000 will equal 7
Answer:
m=0.001k
k=kilometers, m=meters,
Step-by-step explanation:
One thousandth=0.001
0.001 k = 1 m
multiply each side by 7
0.007 k =7 m
Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. James makes $816 per year. How much less each month does James make than Matt?
Which expression represents the amount of money James makes each month?
Which equation represents the scenario?
Answer:
he makes $12 less.
Step-by-step explanation:
$80X12=960 - Matts income for the year
960-816=144 -How much less James makes than Matt per year
144/12=12 - How much less James makes than Mat per month
leave 5 stars and a thanks if it was helpful.
Answer:
Which expression represents the amount of money James makes each month?
✔ (80 – x)
Which equation represents the scenario?
✔ 12(80 – x) = 816
Step-by-step explanation:
The sum of two consecutive integers in one less than three times the smaller integer. Find the two integers
Answer:
i dont see a picture
Step-by-step explanation:
You have prizes to reveal! Go to your garne
)) 3 tons of compost cost $3,840.00. What is the price per pound?
A. (-45, -2), (-48, -1), (-49, 0), (-48, 1), (-45, 2)
B. (-2, -53), (-1, -50), (0, -49), (1, -48) (2, -45)
C. (-2, -45), (-1, -48), (0, -49), (1, -48) (2, -45)
Answer:
(-2)^2 - 49
4 - 49 = -45
(-1)^2 - 49 = 1 - 49= -48
(0)^2-49= 0-49=-49
(1)^2-49=1-49=-48
(2)^2-49= 4-49= -45
the solution is either a or c
(x,y) ==> (-45,-2),(-48,-1),(-49,0),(-48,1),(-45,2)
(y,x)==> (-2, -45), (-1,-48), (-0,-49),(1,-48),(2,-45)
Step-by-step explanation:
A) find the value of C
B) find the value of A
Answer:
a. 31.42
b. 78.55
It`s your ans...
What are the domain and range of f(x)=(1/5)x
Answer:
Step-by-step explanation:
hello :
f(x)=(1/5)x
the domain is : D= ℝ =]-∞ ,+∞[ (linair function)
the range is : E= ℝ =]-∞ ,+∞[ ( f^-1 is linair function)
Dado dos ángulos complementarios, uno mide (2x + 10) y el otro (x + 20),
calcula el valor de x
Answer:
El valor de x es igual a 20 o x = 20.
Step-by-step explanation:
Lo primero que se debe saber es que dos ángulos complementarios suman un ángulo recto o 90º.
Supongamos que el valor de un ángulo [tex] \\ \alpha[/tex] y un ángulo [tex] \\ \beta[/tex] valen:
[tex] \\ \alpha = 2x + 10[/tex] [1]
[tex] \\ \beta = x + 20[/tex] [2]
Como la suma de [tex] \\ \alpha + \beta = 90[/tex] [3]
Entonces
[tex] \\ \alpha + \beta = (2x + 10) + (x + 20) = 90[/tex]
Sumamos los factores comunes entre si:
[tex] \\ (2x + x) + (10 + 20) = 90[/tex]
Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:
[tex] \\ (2 + 1)x + (10 + 20) = 90[/tex]
[tex] \\ 3x + 30 = 90[/tex]
Para despejar la incógnita x, debemos tener en cuenta que una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:
[tex] \\ 3x + 30 - 30 = 90 - 30[/tex]
[tex] \\ 3x + 0 = 90 - 30[/tex]
[tex] \\ 3x = 60[/tex]
Ahora dividimos cada miembro de la igualdad entre 3 (o multiplicamos cada lado de la igualdad por [tex] \\ \frac{1}{3}[/tex] ):
[tex] \\ \frac{3}{3}x = \frac{60}{3}[/tex]
Como sabemos que:
[tex] \\ \frac{3}{3} = 1[/tex]
Entonces:
[tex] \\ 1*x = \frac{60}{3}[/tex]
[tex] \\ x = \frac{60}{3}[/tex]
[tex] \\ x = 20[/tex]
De esta manera, el valor de x es igual a 20 o x = 20.
Lo anterior lo podemos comprobar considerando las ecuaciones [1], [2] y [3]. Así tenemos que:
[tex] \\ \alpha = 2x + 10[/tex] [1]
Sustituimos x por el valor de 20:
[tex] \\ \alpha = 2*20 + 10 = 40 + 10 = 50[/tex]
[tex] \\ \beta = x + 20[/tex] [2]
Hacemos lo mismo para [2]:
[tex] \\ \beta = 20 + 20[/tex]
[tex] \\ \beta = 40[/tex]
De esta manera:
[tex] \\ \alpha + \beta = 90[/tex] [3]
[tex] \\ 50 + 40 = 90[/tex]
Question #5:
Find the area of the composite shape.
30 ft
20 ft
HELP FAST
After spending $2150 for tables and $4050 for chairs, a convention center manager finds that the total is 9% more than he spent
on tables and chairs last year. To the nearest dollar, find the amount that he spent last year.
a. $558
$6813
b. $4451
d. $5688
Please select the best answer from the choices provided
0
A
oo
Mark this and return
Show Me
Save and Exit
Next
Submit
Answer:
D. $5688
Step-by-step explanation:
good luck
what are two numbers that give you the difference of 2 and a sum of 84?
Answer:
41 + 43? I think
Step-by-step explanation:
41 + 43 = 84
43 - 41 = 2
Choose the correct simplification of the expression –5x2(4x – 6x² – 3).
Answer:
[tex]30x^{4} -20x^{3} +15x^{2}[/tex]
Step-by-step explanation:
Simplify using the distributive property.
two people were doing yard work for 1 hour and 35 minutes then they stopped for lunch at 1:20pm at what time did they start doing yard work?
Answer: The answer would be at 11:45.
Step-by-step explanation: First I though, if they stoppedd for lunch at 1:20 and they've been doing yard work for 1 hour and 35 minutes, I would subtract. 1 hour taken away from 1:20 would be 12:20. Then, since it would be hard to subtract 35 minutes from 12:20, 35 minutes - 20 minutes = 15 minutes. 12:20 subtract 20 minutes = 12:00. 12:00 - 15 minutes equal to 11:45. I hope this helps. I know this explanation can be confusing but it's the best I can do at the moment.
PLZ IM TAKING TEST RN. HELP!!!!!!
For two functions, m(x) and p(x), a statement is made that m(x) = p(x) at x = 7. What is definitely true about x = 7? (2 points)
Both m(x) and p(x) cross the x-axis at 7.
Both m(x) and p(x) cross the y-axis at 7.
Both m(x) and p(x) have the same output value at x = 7.
Both m(x) and p(x) have a maximum or minimum value at x = 7.
Answer:
Both m(x) and p(x) have the same output value at x = 7
Step-by-step explanation:
for two functions m(x) and p(x) we know that the solution to the equation :
m(x)=p(x) is the x-value of the point of intersection of the two curves.
i.e. at this point the output value i.e. the value which is obtained on putting the input value i.e. 'x' is same for the two functions m(x) and p(x).
Hope This Helped
When m(x) = p(x) at x = 7, it implies that both functions produce the same output value at x = 7, representing the equality of the functions.
Both m(x) and p(x) have the same output value at x = 7. When m(x) = p(x) at x = 7, it means that both functions produce the same output value at x = 7. This is the defining characteristic of the statement made.
For a given x value of 7, both m(x) and p(x) will yield an identical result, indicating that they are equal at that specific point. This does not necessarily mean they cross the x-axis, y-axis, or have maximum or minimum values at x = 7, but rather that their outputs are the same at this particular x value.
Therefore, the correct statement about x = 7 when m(x) = p(x) is that both m(x) and p(x) have the same output value at x = 7.
Which are solutions of the equation 4x2 - 7x = 3x + 24? Check all that apply.
0
x=
-4
0
x=-3
0
w
0
x=
w/N
0
x=2
0
x = 4
Answer:
all work is shown and pictured
16
Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.
Answer:
The options b) ,c) and e) are correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)[tex](\frac{4}{16})^2[/tex] , c) [tex]\frac{12}{192}[/tex] and e) [tex](\frac{3}{12})^2[/tex]Step-by-step explanation:
Given that a large rectangle has a length of 16 and width of 12.
A smaller rectangle has length of 4 and width of 3
To show the ratio of the area of the smaller rectangle to the area of the larger rectangle:we know that "If two figures are similar, the the ratio of its areas is equal to the scale factor squared"
From the given scale factor is [tex]\frac{1}{4}[/tex]
Let z be the scale factor
Let x be the area of the smaller rectangle
Let y be the area of the large rectangle
[tex]z^2=\frac{x}{y}[/tex]
Since scale factor is [tex]\frac{1}{4}[/tex] hence [tex]z=\frac{1}{4}[/tex]
we have [tex]z^2=(\frac{1}{4})^2[/tex]
[tex]=\frac{1}{16}[/tex]
∴ [tex]z^2=\frac{1}{16}[/tex]
Now show that the ratio of the area of the smaller rectangle to the area of the larger rectangle with each options.
a) [tex]\frac{4}{16}[/tex]
[tex]\frac{4}{16}=\frac{1}{4}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{4}\neq \frac{1}{16}[/tex]
Hence it is not possible.b) [tex](\frac{4}{16})^2[/tex]
[tex](\frac{4}{16})^2=\frac{16}{256}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.c) [tex]\frac{12}{192}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.d) [tex](\frac{4}{12})^2[/tex]
[tex]=\frac{16}{144}[/tex]
[tex]=\frac{1}{9}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{9}\neq \frac{1}{16}[/tex]
Hence it is not possible.e) [tex](\frac{3}{12})^2[/tex]
[tex]=\frac{9}{144}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.∴ options b) ,c) and e) are correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)[tex](\frac{4}{16})^2[/tex] , c) [tex]\frac{12}{192}[/tex] and e) [tex](\frac{3}{12})^2[/tex]Answer:
The other individual who answered the question is correct, please give them 5 stars and a thanks.
Step-by-step explanation:
To simplify and clarify, the answers are B, C, E
In May, Jenna's mean weekly salary was $78. She earned $70 in Week 1, $88 in Week 2, and $67 in Week 3. How much did Jenna earn in the last week of May?
Answer:
just add then all up then divide each of them buy the answer
Step-by-step explanation:
21. Given below are lease terms at the local dealership.
Terms:
• Length of lease = 36 months
• MSRP of the car = $22,500
• Purchase value of the car after lease = $17,500
• Down payment = $1999
• Monthly payment = $425
• $475 security deposit
• $500 acquisition fee
What is the total cash due at signing (including the first monthly payment)?
Answer:
you're answeris $3,399
Answer:
3,399
Step-by-step explanation:
Please Help
I already posted this before but forgot the pic. Also can u show the work please.
Answer:
y-2 = (1/2)(x-4)
Step-by-step explanation:
you already have your slope and points given, just plug them in
** to make things clear, your point (4,2) should be (x1,y1) when you plug into equation
y-2 = (1/2)(x-4)
x2 - 2x = 24
O A 4.8,5
OB 26, -24
Oc 6.-4
C
D
4.8. -4.8
Answer:
6,-4 /is the right answer
Answer:
C. 6, -4.
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x = -4, 6.
please help will give branilest when i can if you help !
Fill in the table with relative frequencies by column
a = 22.4 , 50.0, 66.7 ,72.3
b = 7.9, 17.1, 20.7, 32.6
c = 44.7, 46.7, 83.1, 97.2
d = 27.1, 48.9, 59.0, 80.7
e =17.1, 50.9, 67.4, 82.9
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Answer:
Hey, can you create a clearer question for us to answer please
Step-by-step explanation:
Thanks
:)
Write the following finite decimals as fractions (you do not need to reduce to lowest terms).
1, 1.4, 1.41, 1.414, 1.4142, 1.41421
Answer:
To make any decimal a fraction, you just add a denominator that has one more digit. Ex: .5 has 1 digit. So add 1 zero, and you get 10 as the denominator.
1, 14/10, 141/100, 1414/1000, 14142/10000, 141421/100000
The given decimals can be converted to fractions based on the decimal place values. Therefore, 1 converts to 1, 1.4 to 14/10, 1.41 to 141/100, 1.414 to 1414/1000, 1.4142 to 14142/10000, and 1.41421 to 141421/100000.
Explanation:The numbers given can be written as fractions by considering the place value of the digits after the decimal point. Here is the conversion:
1 can be written as 1/1 or just 1 as there is no decimal part.1.4 can be written as 14/10 because 4 is in the tenths place.1.41 is 141/100 as 1 is in the hundredth place.1.414 can be written as 1414/1000 since 4 is in the thousandths place.1.4142 is 14142/10000 as 2 is in the ten-thousandths place.1.41421 can be written as 141421/100000 because 1 is in the hundred-thousandths place.Learn more about Decimal to Fraction Conversion here:https://brainly.com/question/31738948
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What is the value of quartile 2 (Q2)? 4.7
2.3
3.0
0
Help fast will mark as brainleist
Answer:
[tex]Q_{2}[/tex] = 3.0
Step-by-step explanation:
[tex]Q_{2}[/tex] represents the median of the data set.
From the box plot the median is the horizontal line inside the box and is positioned at 3.0
A basketball coach recorded the number of points his team scored in each of the 11 games they played.
45 68 74 59 69 70 67 77 72 61 75
What is the interquartile range of the data?
A. 5
B. 8
C. 13
D. 15
Answer:
The inter-quartile range is 13. So the answer is C.
Step-by-step explanation:
Answer:
The inter-quartile range is 13. So the answer is C.
(2b - 5)(2b + 5) =?
Please help! Polynomials are difficult for me..
Answer:
(2b-5)(2b+5)
4b^2-25
Step-by-step explanation:
Answer: 4b^2-25 is your answer.
(Vote me brainliest, please)
There are 8 green, 10 purple, 6 red and 16 blue markers in a box. A marker is chosen,replaced and then another marker is chosen. Find the probability that neither marker is red.
The probability that neither marker chosen from the box is red is 72.25%
Explanation:The probability that neither marker chosen is red can be calculated by finding the probability of not picking a red marker twice. There are a total of 40 markers (8 green, 10 purple, 6 red, and 16 blue). Therefore, the probability of not picking a red marker on the first try is 34/40 or 0.85 (since there are 34 non-red markers).
Because the marker is replaced, the conditions remain the same for the second draw. Hence, the probability of also not picking a red marker in the second draw remains at 0.85.
As these are two independent events, the total probability of neither marker being red is found by multiplying the probabilities of the individual events. Hence, 0.85 * 0.85 = 0.7225. Hence the probability that neither marker is red is 0.7225 or 72.25%.
Learn more about Probability here:https://brainly.com/question/32117953
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To find the probability that neither marker is red, calculate the probability of selecting a non-red marker on each draw and multiply the probabilities together.
Explanation:To find the probability that neither marker is red, we need to calculate the probability of selecting a non-red marker on each draw.
The total number of markers in the box is 8 (green) + 10 (purple) + 6 (red) + 16 (blue) = 40.
The probability of selecting a non-red marker on the first draw is (8 + 10 + 16)/40 = 34/40 = 17/20.
Since the marker is replaced back in the box, the probability of selecting a non-red marker on the second draw is also 17/20.
The probability that neither marker is red is the product of the individual probabilities: (17/20) * (17/20) = 289/400.
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A shirt originally cost $52.29, but it is on sale for $36.60. What is the percentage decrease of the price of the shirt? If necessary,
round to the nearest percent.
Answer: 30%
Step-by-step explanation:
A population of 110,000 grows 3% per years 15 years. How much will the population. How much will the population be after 15 years? Terms of x
Answer:
The population be after 15 years is 171376.
Step-by-step explanation:
Given : A population of 110,000 grows 3% per years 15 years.
To find : How much will the population be after 15 years?
Solution :
Exponential growth population model is given by,
[tex]P(t)=P_o(1+r)^t[/tex]
Where,
P(t) is the population at time (t)
[tex]P_o=110,000[/tex] is the initial value of the population
r=3%=0.03 is the annual rate of growth
t=15 is the time in years.
Substitute the value,
[tex]P(t)=110000(1+0.03)^{15}[/tex]
[tex]P(t)=110000(1.03)^{15}[/tex]
[tex]P(t)=110000\times 1.5579[/tex]
[tex]P(t)=171376.41[/tex]
Therefore, the population be after 15 years is 171376.
Final answer:
The future population after 15 years of 3% annual growth starting with a population of 110,000 is calculated using the exponential growth formula, resulting in approximately 171,380 people.
Explanation:
To calculate the future population given a current population, growth rate, and number of years, you can use the formula for exponential growth:
P(t) = P0 ×[tex](1 + r)^{t}[/tex]
Where:
P(t) is the population after t years.
P0 is the initial population.
r is the annual growth rate (expressed as a decimal).
t is the time in years.
In this case, the initial population (P0) is 110,000, the growth rate (r) is 3% or 0.03, and the time (t) is 15 years.
Applying these values to the formula:
P(15) = 110,000 × (1 + 0.03)¹⁵
Now we compute the amount (rounded to the nearest whole number):
P(15) = 110,000 × 1.03¹⁵
P(15) ≈ 110,000 × 1.558
P(15) ≈ 171,380
Therefore, the population after 15 years will be approximately 171,380 people.