You are a new parent and would like to have $100,000 saved for your child’s college
education 18 years from now.
a. How much would you need to invest each year, starting now, to reach your goal
assuming 5% continuous annual interest?
b. What is the present value of that $100,000 when your child is born?
Answers
a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000
b. The present value of $100,000 when your child is born is $100,000.
What is Compound Interest?Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.
a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:
\(FV = PMT*((1 + r)^n - 1)/r\)
where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).
Plugging in the values, we get:
$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05
Solving for PMT, we get:
PMT = $3,436.76
Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.
b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:\(PV = FV/(1 + r)^n\)
where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).
Plugging in the values, we get:
PV = $100,000/(1 + 0.05)^0
Solving for PV, we get:
PV = $100,000
Therefore, the present value of $100,000 when your child is born is $100,000.
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Related Questions
Panjang bayangan pohon oleh sinar matahari adalah 15 m. Pada tempat dan saat yang sama tiang bendera sepanjang 3 m memiliki panjang bayangan 6 m. Tinggi pohon adalah …
Answers
Tinggi pohon / Panjang bayangan pohon = Tinggi tiang bendera / Panjang bayangan tiang bendera
Letakkan variabel h sebagai tinggi pohon. Maka:
h / 15 = 3 / 6
Kali kedua sisi dengan 15, kita dapatkan:
h = (15 x 3) / 6
h = 7.5
Jadi, tinggi pohon adalah 7.5 meter.
7. Which Statement is TRUE? a. 1,-5, 25, -125, ... is a geometric sequence because to get to the next term, you multiply -5 times the previous term. b. 1, 8, 15, 22, 29, ... is a geometric sequence because to get to the next term, you multiply 8 times the previous term. C. 1,-4, -9,-14, ... is a geometric sequence because to get to the next term, you add - 5 to the previous term. d. 1, 1.5, 2, 2.5, is a geometric sequence because to get to the next term, you add 0.5 to the previous term. I.
Answers
the answer is option A
the series is given as 1, -5, 25, -125....
now to test if this is a geometric sequence, let's find the common ratio between two successive numbers
take the fourth term and divide it by the third term
\(-\frac{125}{25}=-5\)take the third term and divide it by the second term
\(\frac{25}{-5}=-5\)take the second term and divide it by the first term
\(-\frac{5}{1}=-5\)from the observation above, they all have a common ratio of -5 and that implies to find the next term, simply multiply the term -5 to the prevoius term
Someone help
A)17/15
B)15/17
C)17
D)8/17
E)17/8
Answers
Answer:
B) 15/17
Step-by-step explanation:
You want the sine of acute angle A in the right triangle shown.
SineThe sine of the angle is the ratio ...
Sin = Opposite/Hypotenuse
We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)
The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.
CheckThe value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.
Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.
The sine of angle A is 15/17.
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Using π = 3.14, what is the circumference of a circle with a diameter of 7 units? Round your answer to the nearest hundredth.
Answers
Answer:
21.98
Step-by-step explanation:
c=2*pie*r
2*3.14*3.5
21.98
approximate 22
:)
Alina's softball coach writes the team's number of games played and number of wins on a board in the locker room as shown, but the number of wins was accidentally erased. The coach knows that the ratio of wins to games played so far this season is equal to 0.8. How many wins does the team have?
A: 3 wins
B: 8 wins
C: 10
D: 12
Answers
Answer:
A
Step-by-step explanation:
what answer? here, can you answer that? thankyou
Answers
It should be noted that the number of sample size based on the information will be 300.
How to explain the sampleIn order to calculate the sample size, we can use the following formula:
n = z² * p * (1-p) / E²
n = 1.96² * 0.5 * (1-0.5) / 0.05²
= 300
A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.
In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".
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Regina deposits $4,500 in a savings account that pays 7 1/2% interest, compounded semiannually. How much interest does the account earn in the second six months?
Answers
Answer:
uh I'm going to say it's 3,000 sorry if I'm wrong
Step-by-step explanation:
Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.
If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.
Answers
The number 100 would land in column 2
The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?Given that we have the array of numbers
The length of each row in the array is 7
Dividing 100 by 7, we have
100/7 = 14 Remainder 2
This means that
Column = 2
In which row would the number 100 land?In (a), we have
100/7 = 14 Remainder 2
This means that
Row = 14
The location of 100 in rows of 6 numbersHere, we have
The length of each row in the array is 6
Dividing 100 by 6, we have
100/6 = 16 Remainder 3
So, the location of 100 in rows of 6 numbers is row 16 and column 3
Predicting the row and column 100 will landLet the length of each row in the array be n
Dividing 100 by n, we have
100/n = q Remainder r
This means that the location of 100 in rows of n numbers is row q and column r
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Daija wants trim 3.5centimetes from her hair how should she move the decimal point to convert this number to millimeters
Answers
9514 1404 393
Answer:
right
Step-by-step explanation:
1.0 cm = 10. mm . . . . . . the decimal point is moved to the right
3.5 cm = 35. mm . . . . . . the decimal point is moved to the right
What number makes the expressions equivalent? Enter your answer in the box.
12 (–1.4m + 0.4) =
m + 0.2
Answers
The number makes the expression equivalent is m = 0.2584.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 12(- 1.4m + 0.4) = m + 0.2.
- 16.8m + 4.8 = m + 0.2.
- 16.8m - m = 0.2 - 4.8
- 17.8m = - 4.6.
m = (-4.6/-17.8).
m = 0.2584.
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Write the equation of the graph
Answers
Answer:
x + 2y - 5 = 0
Step-by-step explanation:
We can see that , the graph passes through (0,2.5) and (5,0) . Therefore the ,
x intercept is 5 y intercept is 2.5We can use the intercept form of equation as ,
=> x/a + y/b = 1
=> x/5 + y/2.5 = 1
=> x + 2y/5 = 1
=> x + 2y = 5
=> x + 2y -5 = 0 .
This equation can be verified by plotting the graph .[ Refer to attachment ]
Hence the equation of the line is x + 2y - 5 = 0 .
all real numbers are irrational numbers?
Answers
Answer:
no.
Step-by-step explanation:
the group of all real numbers consists of both rational and irrational numbers.
GPAs of freshman biology majors have approximately the normal distribution with mean 2.87 and
standard deviation .34. In what range do the middle 90% of all freshman biology majors' GPAs lie?
Answers
Answer:
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 2.87 and standard deviation .34.
This means that \(\mu = 2.87, \sigma = 0.34\)
Middle 90% of scores:
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05. So X when Z = -1.645.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.645 = \frac{X - 2.87}{0.34}\)
\(X - 2.87 = -1.645*0.34\)
\(X = 2.31\)
95th percentile:
X when Z has a pvalue of 0.95. So X when Z = 1.645.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.645 = \frac{X - 2.87}{0.34}\)
\(X - 2.87 = 1.645*0.34\)
\(X = 3.43\)
The middle 90% of all freshman biology majors' GPAs lie between 2.31 and 3.43.
Evaluate the function over the domain {-2, -1, 0, 1, 2}. As the values of the domain
y = 2.5*
increase, do the values of the range increase or decrease?
Answers
The range of the function is {0.16, 0.4, 1, 2.5, 6.25}. With an increase in the value of the domain, the range of the function is increasing.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
The given function is
f(x) = 2.5^x.
Given domain is {-2, -1, 0, 1, 2}.
Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 2.5^x.
When x = -2:
f(-2) = 2.5^(-2)
f(-2) = 0.16.
When x = -1:
f(-1) = 2.5^(-1)
f(-1) = 0.4
When x = 0:
f(0) = 2.5^(0)
f(0) = 1.
When x = 1:
f(1) = 2.5^(1)
f(1) = 2.5
When x = 2:
f(2) = 2.5^(2)
f(2) = 6.25
The range of the function is {0.16, 0.4, 1, 2.5, 6.25}
The values of the range increase with the increase of domain.
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What is another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 ?
Answers
Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer
How to write a compound inequality in another way?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: y + 3 ≥ 2 and y + 3 < 6
To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:
y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:
2 ≤ y+3 and y + 3 < 6
Combine the two:
2 ≤ y+3 < 6
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NEED HELP ASAP!Noah and Lin are each trying to solve the equation x^2-6x+10=0. They know that the solutions to x^2=-1 are i and -i, but they are not sure how to use this information to solve for x in their equation.Show how Noah can finish his work using complex numbers.
Here is Noah's work:
Answers
Let's solve your equation step-by-step.
x2−6x+10=0
For this equation: a=1, b=-6, c=10
1x2+−6x+10=0
Step 1: Use quadratic formula with a=1, b=-6, c=10.
\(x= -b\) ± \(\sqrt{\frac{b^2 -4ac}{2a}\)
x = −(−6)± \(\sqrt{\frac{(-6)^2 -4(1)(10)}{2(1)}\)
x= 6± \(\frac{\sqrt{-4} } {2}\)
x = 6± \((\sqrt{4})( \sqrt{-1} )\) / 2
x = 6 ± \((\sqrt{4})( i )\) / 2
\((\sqrt{4}) = 2\)
6 ± 2i / 2 = 3 ± i
Answer:
Lins
Step-by-step explanation:
Lins took less steps and solving the equation seembes more simple
Use the figure on the right to find the length of DC.
Answers
Answer:
this is the figure btw
Step-by-step explanation:
Seven students were surveyed on the number of hours of TV they watch each week. The results are shown below.
8, 12, 13, 15, 16, 17, 17
What is the mode of the data set?
7
14
15
17
Answers
See attached for the question
Answers
Check the picture below.
Answer:
∠ U = 12°
Step-by-step explanation:
the inscribed angle RST is half the measure of its intercepted arc RT , then
arc RT = 2 × ∠ RST = 2 × 30° = 60°
the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is
∠ U = \(\frac{1}{2}\) ( RS - RT ) = \(\frac{1}{2}\) × (84 - 60)° = \(\frac{1}{2}\) × 24° = 12°
Find the length of x??
Answers
Answer:
8 meters.
Step-by-step explanation:
the formula for the hypotenuse of a right triangle is: \(a^2 + b^2 = c^2\). Where C= hypotenuse and a and b = other sides. We can sub in a and c to get \(6^2 + x^2 = 10^2\\\). Simplify to \(36+x^2=100\). Subtract 36 from both sides to get x^2 = 64. \(\sqrt{64} =8\)
(1/10x−2/3)−(4/5x−1/6)
Answers
Answer:
- 7x + 5/10
Step-by-step explanation:
I used a calculator, please let me know if im incorrect
Can you help me with this question
Answers
Answer:
308 (Third Option)
Step-by-step explanation:
Have a Great Day! :D
...................................................
Answers
Answer:
....................................
Step-by-step explanation:hope i helped
Jerry made his mother a garden. The width is 6
5/7
ft and the length is 7
3/5
ft. What is the area of the garden?
Answers
Answer:
The area of the garden is 51
Step-by-step explanation:
what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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A new is being built in Safety Harbor. The perimeter of the rectangular playing field is 582 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
Answers
The dimensions of the rectangular field are given as follows:
Length: 232 yards.Width: 59 yards.How to obtain the perimeter of a rectangle?The perimeter of a rectangle is given by twice the sum of the length and the width of the rectangle, as follows:
P = 2(l + w).
For this problem, the perimeter is of 582 yards, hence:
2(l + w) = 582
l + w = 291.
The length of the field is 4 yards less than quadruple the width, hence:
l = 4w - 4.
Then the width is obtained as follows:
4w - 4 + w = 295
5w = 295
w = 295/5
w = 59.
The length is obtained as follows:
l = 4 x 59 - 4
l = 232 yards.
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Sasha’s daily tips this work week were $43, $32, $65, $88, $50, and $72. Is Sasha correct in thinking that the mean accurately represents how much money she makes in daily tips? Yes, Sasha is correct. The mean amount she makes is $58.33 in a day. Yes, Sasha is correct. The mean amount she makes is $65.33 in a day. No, Sasha is not correct. The median amount she makes is $53.00 in a day. No, Sasha is not correct. The median amount she makes is $60.00 in a day.
Answers
Answer: $58.33
Step-by-step explanation:
Yes, Sasha is correct. The mean amount she makes is in a day.
Answer:
a: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day
Step-by-step explanation:
edg2020
Find the distance between (2. 10) and. (3. -8)
Answers
Answer:
-18
Step-by-step explanation:
Which of the three side lengths can NOT form a triangle?
(A) 3 ft, 4 ft, 8 ft
(B) 5 in, 5in, 5in
(C) 1 m, 2 m, 1m
(D)2 ft, 4 ft, 5 ft
Answers
The arc marks demonstrate that a triangle cannot be formed by the two sides coming together. According to the Triangle Inequality Theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side.
What is triangle?A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.The sum of the three angles of the triangle is 180 degrees. A triangle is a polygon with three vertices and three sides.The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees. It has the fewest sides of any polygon.The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it.Therefore, the triangle cannot be formed if the three side lengths are 1, 2, and 1.To learn more about triangle, refer to:
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If A, dollars are invested at annual interest rate r, compounded
monthly, then after years the account will have grown to
121
A(t) = 40 (1
10 (1 + )"
12
If $2000 is placed into an account eaming 12% annual
interest, compounded monthly, how much will it grow to after
15 years?
Answers
Answer:
$11,991.60
Step-by-step explanation:
An appropriate formula is ...
A = P(1 +r/n)^(nt)
where r is the annual rate, n is the number of time per year interest is compounded, and t is the number of year. P is the principal invested.
Filling in the given numbers, we have ...
A = $2000(1 +0.12/12)^(12·15) = $2000(1.01^180) ≈ $11,991.60
The account balance after 15 years will be $11,991.60.