The requreid present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.
To find the present value of $700 after 4 years at 11% compounded monthly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]
Substituting the given values, we get:
[tex]700 = P(1 + 0.11/12)^{12*4}[/tex]
Simplifying this equation, we get:
[tex]P = 700 / (1 + 0.11/12)^{12*4}\\P = 700 / (1.00917)^{48}[/tex]
P = 700 / 1.487
P = 451.73
Therefore, the present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.
Learn more about present value here:
https://brainly.com/question/17322936s
#SPJ1
Jack went for a mountain hike. On his way up, he traveled
at a speed of 2 mph. He reached the summit in 3 hours. On his
way back down, Jack jogged at a speed of 5 mph. Write
the formula that describes how the distance Jack covered during
the hike depends on the amount of time that he traveled.
Answer:
d = (20/7)t
Step-by-step explanation:
You want the distance traveled as a function of travel time if Jack's speed going up was 2 mph and going down was 5 mph.
TimeThe relation between time, speed, and distance is ...
t = d/s
If the total distance is d, the total travel time up and back is ...
t = t1 +t2
t = (d/2)/(2) +(d/2)/5 = d(1/4 +1/10) = 0.35d
Solving for distance, we have ...
d = t/0.35
d = (20/7)t . . . . miles, where t is in hours
<95141404393>
35% of those falled will find an excuse to avoid jury duty. if 10 people are called for jury duty, then what is the probability that 2 will find an excuse
The evaluated probability that 2 will find an excuse is 12.8%, under the condition that 35% of those failed will evaluate an excuse to avoid jury duty.
According to the data I found, about 23% of those evaluated to find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.
In the event 10 people are called for jury duty, then the evaluated probability that 2 will find an excuse can be found out using the binomial probability distribution formula.
The formula is:
[tex]P(X=k) = C(n,k) * p{^k }* (1-p)^{(n-k)}[/tex]
Here,
P(X=k) = successes probability of k in n trials
C(n,k) = combinations of number in n things taken k at a time
p= success probability of any one trial
n = trial number
For the given case
k = 2
n = 10
p = 0.23
Staging these values into the formula
[tex]P(X=2) = C(10,2) * 0.23^{2}* (1-0.23)^{(10-2)}[/tex]
= 45 × 0.0529 × 0.5225
= 0.128
Hence, the probability that exactly 2 out of 10 people will evaluate an excuse to avoid jury duty is 0.128 or approximately 12.8%.
To learn more about probability
https://brainly.com/question/13604758
#SPJ1
Find the two perfect squares that each Integer is between. Then approximate the square root to one decimal place.
√47
pls i need it quick
Answer:
[tex] 36 < 47 < 49[/tex]
[tex] \sqrt{36} < \sqrt{47} < \sqrt{49} [/tex]
[tex]6 < \sqrt{47} < 7[/tex]
√47 is approximately 6.9
Determine the measure of the arc CED
Answer:kbef;eohrjkvoubwe
cv bojbDetectives are unsure whether Kendall Postwell will be able to testify at her trial. They say it is a question of competence. What does this MOST likely mean?
A.
Kendall might be determined to be insane and not qualified to testify.
B.
The evidence in Kendall’s case is inconclusive and doesn’t prove anything.
C.
Kendall is an expert witness who has testified many times before.
D.
The police think it will hurt their case if Kendall chooses to testify.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Arc length= [tex]\frac{interior angle}{360} 2\pi r[/tex]
un automóvil que se desplaza en una pista recta aumenta su velocidad de 15 m/s a 45 m/s utilizando para ello un
po de 10 segundos. Consideremos que la aceleración fue uniforme, calcula:
aceleración en dicho tiempo.
The acceleration of the car at that time was 3 m/s².
We have,
From the kinematic equation to find the acceleration:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Initial velocity u = 15 m/s
Final velocity v = 45 m/s,
Time t = 10 s
We can rearrange the equation to solve for acceleration:
a = (v - u) / t
Substituting the values, we get:
a = (45 m/s - 15 m/s) / 10 s
a = 3 m/s^2
Therefore,
The acceleration of the car at that time was 3 m/s².
Learn more about accelerations here:
https://brainly.com/question/30581474
#SPJ1
The complete question in english.
A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a
po of 10 seconds. Assuming that the acceleration was uniform, calculate:
acceleration at that time.
Which set of data contains two outliers?
113, 115, 103, 114, 109, 111, 119
141, 151, 138, 142, 149, 140, 150
99, 113, 91, 104, 109, 114, 97
101, 135, 131, 99, 138, 136, 140
Answer:
D.
Step-by-step explanation:
The set of data that contains two outliers is: 101, 135, 131, 99, 138, 136, 140. An outlier is a value that is significantly different from other values. In this set, both 99 and 138 are outliers because they are much lower and higher respectively than the other values. In the other sets, all values are relatively close to each other with no extreme deviations, thus they do not contain any outliers. Outliers can skew statistical analyses and should be removed or treated with caution.
Step-by-step explanation:
The set of data containing two outliers is the last one: 101, 135, 131, 99, 138, 136, 140. This can be determined by analyzing the range and distribution of the data. Two values, 99 and 140, are significantly different from the other values in the set and fall outside the typical range. These two extreme values are considered outliers and can impact the accuracy of any analysis or Scalculations based on the data.
What is the sum of the interior angle
measures of a regular hexagon? Show
or explain how you can use the sum
of the interior angles of a triangle to
determine the answer.
The sum of the interior angle of the regular hexagon is S = 720°
Given data ,
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
when n = 6 for a hexagon , we get
nθ = 180 ( 6 - 2 )
nθ = 180 x 4
nθ = 720°
Hence , the sum of interior angles of a hexagon is 720°
To learn more about sum of the interior angles of a polygon click :
https://brainly.com/question/14611583
#SPJ1
The radius of a circle is decreasing at a constant rate of 2 centimeters per second. What is the rate of change of the area of the circle, in square centimeters, at the instant that the radius, r=5 centimeters
The rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.
Use the formula A=pi*r^2 to calculate the area of the circle when the radius is 44cm.
A=pi*r^2
A= 3.14159*(44 cm)^2
A= 6081.816 cm^2
Use the formula A'=2pi*r*r' to calculate the rate of change of the area.
A'=2pi*r*r'
A'= 2*3.14159*44 cm*(7 cm/s)
A'= 97.636 cm^2/s
The area of a circle is calculated by the equation A=pi*r^2, where r is the radius of the circle. At the instant when the radius of the circle is 44 centimeters, the area is 6081.816 cm^2.
To calculate the rate of change of the area, we use the equation A'=2pi*r*r', where r' is the rate of change of the radius.
In this case, the radius of the circle is decreasing at a rate of 7 cm/s, so r'=7 cm/s. Plugging these values into the equation, we get A'=2*3.14159*44 cm*(7 cm/s), which equals 97.636 cm^2/s.
Therefore, the rate of change of the area of the circle is decreasing at a rate of 97.636 cm^2/s when the radius is 44 cm.
Learn more about radius here
brainly.com/question/15047456
#SPJ1
complete question:
the radius of a circle is decreasing at a constant rate of 7 centimeters per second. at the instant when the radius of the circle is 44 centimeters, what is the rate of change of the area? round your answer to three decimal places.
If a player bets 3$ on the 5$ denomination, find the players expectation
The player can expect to win 1.67$ for each 3$ bet placed on the 5$ denomination.
In probability theory, the expected value or expectation is the value that a player would expect to receive on average if they repeated the same game many times under the same conditions.
To find the player's expectation, we need to use the formula:
Expectation = (Probability of Winning x Amount Won) - (Probability of Losing x Amount Lost)
Assuming that the player wins if the bet is successful, the probability of winning on a 5$ denomination bet is 1/3, since there are three possible outcomes (win, lose, or push). The probability of losing is 2/3, since the player will lose if the bet is unsuccessful or if the outcome is a push.
If the player bets 3$ on a 5$ denomination, there are two possible outcomes: they either win 5$ or lose 3$. Therefore, the player's expectation can be calculated as:
Expectation = (1/3 x 5$) - (2/3 x 3$) = 1.67$
To learn more about denomination click on,
https://brainly.com/question/25308871
#SPJ1
PQ is tangent to Circle O at Point P with arc lengths 160° and 60° as shown below.
The measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula. So option A is correct.
What is the secant tangent angleThe secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:
θ = 1/2 (arc EB - arc BD)
where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.
From the question,
θ = m∠PQR
arc EB = 160°
arc BD = 60°
m∠PQR = 1/2(160° - 60°)
m∠PQR = 1/2 × 100°
m∠PQR = 50°
Therefore, the measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula.
Read more about secant tangent here:https://brainly.com/question/9132922
#SPJ1
Use grid paper to find the median of the data. Then find the median of the lower half and the median of the upper half of the data.
82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85
The median is
.
The median of the lower half of the data is
.
The median of the upper half of the data is
.
.
The median is 81.5.
The median of the lower half of the data is 67.
The median of the upper half of the data is 92.
Given a data set,
82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85
Median of a data set is the middle element when the data are arranged in a order.
Arranging in ascending order,
51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98
There are even number of data sets.
So, Median = Average of the middle two elements.
Median = (81 + 82) / 2 = 81.5
Lower half of the data set is,
51, 56, 62, 72, 79, 81
Median = (62 + 72) / 2 = 67
Upper half of the data set is,
82, 85, 89, 95, 97, 98
Median = (89 + 95) / 2 = 92
Hence the median is 81.5, lower half median is 67 and upper half median is 92.
Learn more about median here :
https://brainly.com/question/28060453
#SPJ1
22. Florida has a population of about
2 x 107. The Earth has a population
of about 8 x 10⁹. About how many
times more populated is the Earth
than Florida? Express your answer as a
whole number.
s
Answer:7
Step-by-step explanation:
1. Expand and simplify the following:
a) (x+3)(x + 5)
b) (x-6) (x + 7)
2. Common factor each of the following.
a) 2x+6
b) 9x² - 12x
3. Factor the following difference of squares.
a) x²-121
b) 4x² - 49
4. Factor each of the following trinomials.
a) x² - 10x + 16
b) x²-5x-24
c) (2x-3)(5x-4)
c) 24x² + 16x-2
c) 144-25x²
c) x² +8x-20
5. Factor the following quadratics using the appropriate factoring method (s).
a) 3x² + 18x+24
b) 99-11x²
c) 6x²-48x-54
The Common factor:
a) 2x+6 = 2(x+3)
b) 9x² - 12x = 3x(3x - 4)
How to solveExpand and simplify:
a) [tex](x+3)(x+5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15[/tex]
b) [tex](x-6)(x+7) = x^2 + 7x - 6x - 42 = x^2 + x - 42[/tex]
Common factor:
a) 2x+6 = 2(x+3)
b) 9x² - 12x = 3x(3x - 4)
Factorization is the process of expressing a number or equation in terms of its factors, which are integers or individual terms that when combined together generate the original number or expression. This is an essential concept in algebra and number theory.
Read more about factorization here:
https://brainly.com/question/25829061
#SPJ1
___ less than 60 greater than ___
Answer:
less than 60 is 59 and greater than 60 is 61
Answer:40 and 20
Step-by-step explanation: Mathematically the first fill in the blank can be any number less than 60 here in I have taken it as 40.In the second fill in the blank the it can be any number less than 40 so 20 can be answer I hv chosen here.
The graph below was obtained by transforming the graph of the
square root function. Write the equation for the function the
graph represents.
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x-1)} +2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.Therefore, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 2) + 2
[tex]g(x) = -\sqrt{9(x-1)} +2[/tex]
Read more on translation here: brainly.com/question/4521517
#SPJ1
Question in picture. Solve please.
Answer:
[tex] \frac{1}{3} \pi( {3.5}^{2} )(11) = 44.9\pi[/tex]
C is the correct answer.
) F= {mango, apple) is a given set of fruits. (i) Find the number of subsets of the set F by using formula. (ii) Write all possible subsets of the set F (iii) Among these subsets, which one is the improper subset? Write with reason.
The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.
Given :
The set of days of the week.
The following steps can be used in order to determine the number of subsets and the number of proper subsets:
Step 1 - According to the given data, the set is given below:
S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Step 2 - Now, the total number of subsets is given by the formula where 'n' is the number of elements of the set.
The total number of subsets is 128.
Step 3 - Now, the total number of proper subsets is given by the formula where 'n' is the number of elements of the set.
The total number of proper subsets is 127.
a) The total number of subsets is 128.
b) The total number of proper subsets is 127.
For more information on subsets click:
brainly.com/question/2094789
#SPJ1
complete question:
Find (a) the number of subsets and (b) the number of proper subsets of the set.
The set of days of the week.
(a) The number of subsets is
(b) The number of proper subsets is
What's the solution to the inequality x^2 + 2x < or equal to 24?
a) (-infinity, -6] union [4, +infinity)
b) (-6, 4)
c) (-infinity, -6) union (4, +infinity)
d) [-6, 4]
The solution to the inequality x² + 2x ≤ 24 is D. [-6, 4].
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
x² + 2x ≤ 24
x² + 2x - 24 ≤ 0
x² + 6x - 4x - 24 ≤ 0
x(x + 6) - x(x + 6) ≤ 0
(x + 6)(x - 4) ≤ 0
x = -6 or x = 4.
Read more on quadratic functions here: brainly.com/question/29499209
#SPJ1
It is possible to have a function f:A→B with an element b∈B so that f does not assign any element to b?
Answer:
Yes, it is possible to have a function f:A→B with an element b∈B so that f does not assign any element to b. This happens when b is not in the range of f 1.
I hope this helps!
Ayudaaaaaaaaaaaa
Porfi y gracias
Answer: option b
Step-by-step explanation:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.22
.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 99%
confidence level with an error of at most 0.03
? Round your answer up to the next integer.
A sample size of 176 tenth graders would be needed in order to estimate the fraction of students with reading skills at or below the eighth grade level at a 99% confidence level having an error of at most 0.03.
To calculate the sample size required for estimating the fraction of tenth graders with reading skills at or below the eighth grade level, we can use the formula for sample size estimation for proportions;
n = (ZZ × p × (1 - p)) / (EE)
where; n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, the Z-score for a 99% confidence level, which is approximately 2.626)
p = estimated population proportion (in this case, 0.22)
E = desired margin of error (in this case, 0.03)
Plugging in the given values;
n = (2.6262.626 × 0.22 × (1 - 0.22)) / (0.030.03)
n = 0.15774 / 0.0009
n ≈ 175.27
Since we need to round up to the next integer, the sample size required would be 176.
To know more about sample size here
https://brainly.com/question/30885988
#SPJ1
I'll MARK THE BRAINLIEST!
The line plots show the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week. A) Which statement is true about the range? B) Which statement is true about the mean?
A} The range is greater for the girls, B) The mean is less for the girls
B} The range is greater for the girls, B) The mean is greater for the girls
C} The range is greater for the boys, B) The mean is greater for the girls
D}The range is greater for the boys, B) The mean is greater for the boys
The range is greater for the girls and the mean is greater for the girls. So, correct option is B.
A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.
Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.
B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:
(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours
To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:
(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours
Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".
So, correct option is B.
To learn more about line plot click on,
https://brainly.com/question/12279622
#SPJ1
How is y=4(2)^x-3 translated from the graph of y=4(2)^x
The graph of y=4[tex](2)^{x}[/tex]-3 is the same as the graph of y=4[tex](2)^{x}[/tex] shifted downwards by 3 units.
The function y=4[tex](2)^{x}[/tex] is an exponential function with base 2 and vertical intercept at (0, 4).
To translate this function to the graph of y=4[tex](2)^{x}[/tex]-3, we need to shift the graph downwards by 3 units. This can be achieved by subtracting 3 from the original function as follows:
y = 4[tex](2)^{x}[/tex] - 3
Now, the vertical intercept of the new function y=4[tex](2)^{x}[/tex]-3 is at (0, 1), which is 3 units below the intercept of the original function.
Notice how the entire graph has shifted down by 3 units, while maintaining the same shape as the original exponential function y=4[tex](2)^{x}[/tex].
To learn more about graph here:
https://brainly.com/question/30716175
#SPJ1
Points S and T are midpoints of the sides of trisngle FGH.
The length of GF is 4 cm minus half the length of side FH.
To do this, we can use the fact that point S is the midpoint of FH. This means that FS = 1/2 FH. Similarly, point T is the midpoint of GH, so TG = 1/2 GH. We can now use these equalities and the fact that SG = 4 cm and HT = 6 cm to set up an equation involving FH:
SG + GF + HT = ST + TG + FH
Substituting the given values and using the fact that TG = GH - TG = GH - 1/2 GH = 1/2 GH, we get:
4 cm + GF + 6 cm = 8 cm + 1/2 GH + FH
Simplifying and substituting FS = 1/2 FH and TG = 1/2 GH, we get:
10 cm + GF = 8 cm + FS + TG
GF = 8 cm + FS + TG - 10 cm
GF = 1/2 FH - 1/2 GH
Now, substituting the values we know, we get:
GF = 1/2 FH - 1/2 GH
GF = 1/2 (FS + SH) - 1/2 (GH)
GF = 1/2 (8 cm + SH) - 1/2 (GH)
GF = 1/2 (8 cm + FS) - 1/2 (GH)
GF = 1/2 (8 cm + 1/2 GH) - 1/2 (GH)
GF = 3 cm - 1/4 GH
We can now substitute TG = 1/2 GH and solve for GH:
TG = 1/2 GH
8 cm - FS = 1/2 GH
GH = 16 cm - 2 FS
Substituting this value into the expression for GF, we get:
GF = 3 cm - 1/4 (16 cm - 2 FS)
GF = 3 cm - 4 cm + 1/2 FS
GF = 1/2 FS - 1 cm
Finally, substituting FS = 8 cm - SH, we get:
GF = 1/2 (8 cm - SH) - 1 cm
GF = 4 cm - 1/2 SH
To know more about midpoint here
https://brainly.com/question/28224145
#SPJ1
Complete Question:
Points S and T are midpoints of the sides of triangle FGH
when HT = 6cm, ST = 8 cm, SG = 4CM
what is GF ?
a density graph for all the possible speeds bwtween 0 and 160 is in the shape of a triangle. what’s the height of the triangle
Answer:
0125
Step-by-step explanation:
The answer is equal to 0125
3/10+63/100 what is this
Answer:
The answer would be 0.93!
Step-by-step explanation:
Crown Heights Ceramics collects 6% sales tax on all sales. If total sales including tax are $2739.45 , find the portion that is the tax amount. (Show your work)
$165.60
$164.37
$155.06
$2584.39
If total sales including tax are $2739.45 , the portion that is the tax amount is $155.06. So, correct option is C.
To find the portion that is the tax amount, we need to first determine the portion of the total sales that is the cost of the item before taxes. To do this, we can use the fact that the sales tax is 6%, which means that the total sales including tax is 106% of the cost before taxes.
Thus, we can set up the equation:
total sales including tax = cost before taxes + tax amount
Or, in terms of percentages:
106% cost before taxes = cost before taxes + tax amount
Simplifying this equation, we get:
0.06 cost before taxes = tax amount
Now we can substitute the given information into this equation. If total sales including tax are $2739.45, then the cost before taxes is:
cost before taxes = total sales including tax / 1.06
cost before taxes = $2584.39
Finally, we can calculate the tax amount:
tax amount = 0.06 * $2584.39
tax amount = $155.06
Therefore, the answer is option C, $155.06.
To learn more about tax click on,
https://brainly.com/question/22953434
#SPJ1
State Inc. decides to issue 10% annual coupon bonds with a maturity of 20 years.
a) Using $1,000 as the face value, what should you pay for this bond if the yield to maturity is 12%? If 10%? If 8%? If 6%. Explain the results.
b) Instead, they decide to borrow $50 million from a bank with a maturity of 5 years. If the interest rate is 8%, what is the monthly payment? What is the balance at the end of 28 months?
The bond price at 12% maturity is $435.42, at 10% maturity is $500.00, at 8% maturity is $607.28, and at 6% maturity is $748.65. The balance at the end of 28 months is approximately $41,097,019.67.
To determine the price of the bond at different yield to maturity rates, we need to use the bond pricing formula
Bond price = (Coupon payment / (1 + YTM)¹) + (Coupon payment / (1 + YTM)²) + ... + (Coupon payment + Face value) / (1 + YTM)ⁿ
Where Coupon payment = Annual coupon rate x Face value
YTM = Yield to maturity
n = Number of years to maturity x Number of coupon payments per year
Using $1,000 as the face value and an annual coupon rate of 10%, we have
At 12% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.12)¹) + ($100 / (1 + 0.12)²) + ... + ($100 + $1,000) / (1 + 0.12)⁴⁰
Bond price = $435.42
At 10% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.10)¹) + ($100 / (1 + 0.10)²) + ... + ($100 + $1,000) / (1 + 0.10)⁴⁰
Bond price = $500.00
At 8% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.08)¹) + ($100 / (1 + 0.08)²) + ... + ($100 + $1,000) / (1 + 0.08)⁴⁰
Bond price = $607.28
At 6% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.06)¹) + ($100 / (1 + 0.06)²) + ... + ($100 + $1,000) / (1 + 0.06)⁴⁰
Bond price = $748.65
To calculate the monthly payment and balance of the loan from the bank, we can use the formula for the monthly payment of an amortizing loan
P = (r × A) / (1 - (1 + r)⁻ⁿ)
where P is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), A is the loan amount, and n is the total number of months in the loan.
First, we need to calculate the values of r, A, and n
r = 0.08 / 12 = 0.00667 (monthly interest rate)
A = $50,000,000 (loan amount)
n = 5 years × 12 months/year = 60 months (total number of months in the loan)
Now, we can plug these values into the formula to calculate the monthly payment
P = (0.00667 × $50,000,000) / (1 - (1 + 0.00667)⁻⁶⁰)
P ≈ $1,029,299.29
Therefore, the monthly payment on the loan is approximately $1,029,299.29.
To find the balance at the end of 28 months, we can use the formula for the remaining balance of an amortizing loan
B = (P * (1 - (1 + r)⁻ⁿ')) / r
where B is the remaining balance, r is the monthly interest rate, P is the monthly payment, and n' is the number of months remaining in the loan (which is equal to the total number of months minus the number of months already paid).
After 28 months, the number of months remaining in the loan is
n' = 60 - 28 = 32
We can now plug the values of P, r, and n' into the formula to find the balance
B = ($1,029,299.29 × (1 - (1 + 0.00667)⁻³²)) / 0.00667
B ≈ $41,097,019.67
Therefore, the balance at the end of 28 months is approximately $41,097,019.67.
To know more about bond price here
https://brainly.com/question/15518377
#SPJ1
A total of $7000 is invested: part at 8% and the remainder at 12%. How much is invested at each rate if the annual interest is $580
?
The amount of $5000 is invested at 12% and $2000 is invested at 8%.
Let x be the amount invested at 8% and y be the amount invested at 12%. We know that the total amount invested is $7000, so we have:
x + y = 7000
We also know that the annual interest earned is $580. The amount of interest earned from the investment at 8% is 0.08x, and the amount of interest earned from the investment at 12% is 0.12y. So we have:
0.08x + 0.12y = 580
We now have two equations with two variables. We can solve for one variable in terms of the other in the first equation and substitute it into the second equation:
x = 7000 - y
0.08(7000 - y) + 0.12y = 580
560 - 0.08y + 0.12y = 580
0.04y = 20
y = 500
So $5000 is invested at 12% and $2000 is invested at 8%.
To know more about an annual interest follow
https://brainly.com/question/23121394
#SPJ1
Are △ABC and △DEF similar triangles? Choose all that apply.
No, the corresponding angles are not congruent.
No, the corresponding angles are not congruent.,
No, the corresponding sides are not proportional.
No, the corresponding sides are not proportional.,
Yes, the corresponding sides are proportional.
Yes, the corresponding sides are proportional.,
Yes, the corresponding angles are all congruent.
Answer:
Step-by-step explanation:
No, the corresponding angles are not congruent.,
They have to be EXACTLY the same.
Lol i am learning this to.