Find the deposit required to accumulate $7700 after investing 3 years in an account that pays an APR of 5% compounded quarterly. How much is earned in interest?
Answers
Answer:
The deposit required is $6633.62 and the interest earned is $366.38
Step-by-step explanation:
Compound interest occurs when the interest earned is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
\({\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}\)
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It's given the final amount A=$7700 after t=3 years of investment in an account that pays an APR of r=5%=0.05. Since the interests compound quarterly and there are 4 quarters in a year, then n=4.
To find the principal P, we solve the previous equation for P as follows:
\({\displaystyle P=A\left(1+{\frac {r}{n}}\right)^{-nt}}\)
Substituting:
\({\displaystyle P=7700\left(1+{\frac {0.05}{4}}\right)^{-4\cdot 3}}\)
\({\displaystyle P=7700\left(1+0.0125}\right)^{-12}}\)
P=$6633.62
The interest earned is:
I = A - P = $7700 - $6633.62 = $366.38
The deposit required is $6633.62 and the interest earned is $366.38
Related Questions
please I need help on question 6
Answers
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis against using a random sample of specimens. Calculate the P-value if the observed statistic is . Suppose that the distribution of the sample mean is approximately normal.
Answers
Complete question :
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0 : μ = 12 against H1 : μ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is xbar = 11.5. Suppose that the distribution of the sample mean is approximately normal.
Answer:
0.02275
Step-by-step explanation:
Given :
Population mean μ = 12
Standard deviation, σ = 0.5
Sample size, n = 4
Observed statistic, xbar = 11.5
H0 : μ = 12
H1 : μ < 12
The test statistic = (xbar - μ) ÷ σ/sqrt(n)
Test statistic =. (11.5 - 12) ÷ 0.5/sqrt(4)
Test statistic = - 0.5 ÷ 0.5/2
Teat statistic = - 0.5 / 0.25 = - 2
Since, it is stated that, distribution is approximately normal ; then we can use the Z distribution and obtain our Pvalue.
We could obtain P value using the Pvalue Z distribution calculator at α = 0.05, 1 - tail
Pvalue = 0.02275
Or
P(x < - 2) = 0.02275 (Z distribution table)
A fair coin is flipped 15 times. What is the probability that you will have 5 tails?
Answers
Answer:
9.18%
Step-by-step explanation:
The probability of getting a tail on a fair coin flip is 0.5, and the probability of getting a head is also 0.5. Since each coin flip is independent, we can use the binomial probability formula to calculate the probability of getting exactly 5 tails in 15 flips:
P(X = 5) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5)
where (15 choose 5) is the number of ways to choose 5 tails out of 15 flips, which can be calculated as:
(15 choose 5) = 15! / (5! * 10!) = 3003
Substituting the values, we get:
P(X = 5) = 3003 * (0.5)^15 ≈ 0.0918
Therefore, the probability of getting exactly 5 tails in 15 coin flips is approximately 0.0918 or 9.18%.
In each diagram, one square unit represents 10 square centimeters. Find the area of each figure. Round to the nearest tenth if necessary.
Answers
Answer:
Step-by-step explanation:
A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answers
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
Given h(x)=-x+1, find h(2)
Please Help me!!!!
Answers
just replace x with 2
h(x) = - x+ 1
find h(2):
h(2) = -2 + 1
h(2) = -1
What is the domain of the function y=3x-1?
Please help
Answers
Answer:
what you marked blue is right
Step-by-step explanation:
I think
This shaded shape is made using two semicircles. One semicircle has a diameter of 20cm. The other has a diameter of 30cm.
Answers
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Brian ran 5/6 mile in the morning and 2/3 mile in the afternoon. Did Brian run farther in the morning or in the afternoon?
Answers
Answer:
In the morning
Step-by-step explanation:
Because in the afternoon, he ran 2/3 mile and that is equal to 4/6 which is less than 5/6.
In a group of students, 30 played chess, 19 played volleyball, 25 played
basketball, 14 played both volleyball and chess, 8 played both baskethall
and volleyball, 15 played both basketball and chess and 5 played both
three events. How many played chess only, basketball only and volleyball
only? How many students are there in all?
Answers
Answer:
Explained below.
Step-by-step explanation:
Denote the events as follows:
C = chess
V = volleyball
B = basketball
The data provided is as follows:
n (C) = 30
n (V) = 19
n (B) = 25
n (C ∩ V) = 14
n (B ∩ V) = 8
n (B ∩ C) = 15
n (C ∩ V ∩ B) = 5
Consider the Venn diagram below.
The number of students who played only chess is marked in pink:
n (Only C) = 6
The number of students who played only volleyball is marked in blue:
n (Only V) = 2
The number of students who played only basketball is marked in orange:
n (Only B) = 7
The number of students who played all three is marked in grey:
n (C ∩ V ∩ B) = 5
Given the triangle ABC at points A = ( 2, 2 ) B = ( 4, 5 ) C = ( 6, 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
Answers
To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:
1. Reflect A over the y-axis to get A': (-2, 2)
2. Reflect A' over the x-axis to get A'': (-2, -2)
Therefore, the new point A'' is (-2, -2).
1. Select all equations that have two solutions.
A.x² = 16
B. 4x² = 0
C. x² = -16
D. 3x + 2 = 14
Ex² - 1 = 24
F) (x + 8) (x - 8) = 0
Answers
A) x² = 16 (solutions: x = 4, x = -4)
B) 4x² = 0 (solutions: x = 0)
F) (x + 8)(x - 8) = 0 (solutions: x = -8, x = 8)
evaluate the expression when y=10. 2+y+11
11
12
21
23
Answers
Answer:
23
Step-by-step explanation:
First, we can rearrange the equation to make it look simpler.
2+y+11 ---->
y+2+11
Then, we can combine like terms, thus
y+13
Then, we can plug in 10 for y
(10)+13
Combine like terms again, and the answer is:
23
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold have been of the basic model. Of those buying the basic model, 30% purchase an extended warranty, whereas 50% of all deluxe purchasers do so. If a randomly selected purchaser has an extended warranty, what is the probability that he/she has a basic model?
Answers
W = extended warranty
B = basic model
D = deluxe model
P(W) = P(B and W) + P(D and W) = 0.4*0.3+0.6*0.5 =0.42
P(B|W) = P(B and W) / P(W) = 0.12/0.42
1. Quadrilateral LBMN is the result of a 180 degree rotation of Quadrilateral ABCD around point B, write the corresponding angles and segments in the table below.
Answers
In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,
∠A = ∠L, ∠D =∠M , ∠C = ∠N , and
AB = LB , CD = NM , DA = ML.
Quadrilateral ABCD rotates 180 degrees around point B,
New quadrilateral formed named LBMN
The corresponding angle after rotation of 180 degrees around B is equals to,
B remain at same position.
A rotates and point L take the position of A.
D rotates and point M take the position of D.
C rotates and point N take the position of C.
Corresponding angle to A is angle L.
Corresponding angle to D is angle M.
Corresponding angle to C is angle N.
Similarly corresponding segments are of ABCD and LBNM are
Line segment AB corresponds to line segment LB.
Line segment CD corresponds to line segment NM
Line segment DA corresponds to line segment ML.
Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.
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On a bus, the lady sitting in front of me silently passed gas, but why did my mom (who was sitting next to me) silently ask me "did you pass gas" and accuse me??
Answers
Answer: lol she was lowkey trying to call out the lady in front of you without directly addressing her. Or she was just trying to mess with you cuz that's how moms are
Step-by-step explanation:
1. Lindsey is designing a stained glass window using parallelograms. She draws a model before starting her work. In her model, BCGF and CDHG are parallelograms and BC ≅CD. Find all the segments that are congruent to KG
A. KD, CJ
B. KD
C. KD, CJ, JF, KH, JG
D. KD, CJ, JF
2. Determine whether the statement is always, sometimes, or never true. Explain your reasoning.
In parallelogram MNPQ, the diagonals MP and NQ meet at R with MP=2RP
A. Always. Diagonals of a parallelogram bisect each other.
B. Sometimes. MR¯¯¯¯¯¯¯¯¯ and RP¯¯¯¯¯¯¯¯ may or may not be congruent.
C. Never. The relationship between MP and RP should be MP=3RP.
D. Never. Diagonals of a parallelogram do not bisect each other.
Answers
Answer:
D: KD, CJ, JF
Step-by-step explanation:
I just took the quick check and it was right.
a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.
Represent a⃗ +b⃗ by using the head to tail method.
Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.
To use the Vector tool, select the initial point and then the terminal point.
Answers
The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,
a + b = < 3, -5 >
The graph of the vector sum is given below.
The addition of vectors suggests the addition of the corresponding components of the involving vectors.
Given the vectors are:
a = < 4, - 3 >
b = < - 1, - 2 >
So doing vector addition we get,
a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>
Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.
Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,
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Answer: Look at the image below
Step-by-step explanation: I took the test.
Step 1: Select Vector
Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)
Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)
Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)
Your answer should now look like mine, now go get that A.
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
Answers
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Isabelle collects hats and shoes. After collecting 18 hats this year, she had 39 hats and 49 shoes.
Which shows how to find the number of hats she started off with at the beginning of the year?
OA. 18 x 49
ОВ.
39 - 18
OC.
18 + 39
OD
49 + 18
Answers
Answer:
39-18
Step-by-step explanation:
39-18=21
Find the Central Angle
mXY = = 18 in
radius ZY = 7.64 in
Answers
The central angle is approximately 2.357 radians.
To find the central angle, we can use the formula:
Central angle (θ) = arc length ÷ radius
Given:
Arc length (mXY) = 18 in
Radius (ZY) = 7.64 in
Plugging in the values:
Central angle (θ) = 18 in ÷ 7.64 in
Calculating the division:
θ ≈ 2.357 radians
Therefore, the central angle is approximately 2.357 radians.
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If there are 52 successful outcomes in a sample with a size of 80, what is the
sample proportion?
A. 0.36
B. 0.72
C. 0.52
D. 0.65
Answers
Answer:
D. 0.65
Step-by-step explanation:
divide 52 by 80.
52/80 = 0.65
Answer:
it's 0.65
Step-by-step explanation:
to find the percentage you just divide the successful outcomes by the amount of tries.
52 / 80 is 0.65
What is the distance from C to B
please help me
Answers
I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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MARKING AS BRAINLIST PLEASE HELP!!
Answers
The correct probability that either event will occur is 0.533.
What is probability?A measure of the likelihood of an event to occur.
P(A or B) = P(A) + P(B).
Probability = Number of favorable outcomes/Total number of outcomes
P(A) = 1/5 = 0.3
P(B) = 1/3 = 0.33
P(A) + P(B) = 1/5 +1/3
= 0.533
Probability = 0.533.
Therefore, the probability that either event will occur is 0.533.
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In a board game, each player must roll a number cube and spin a spinner. The number cube is labeled with the numbers 1 through 6 and the spinner consists of eight equal parts shown below. What is the probability you will roll a 5 and land on blue?
A: 1 over 12
B: 1 over 10
C: 5 over 12
D: 2 over 3
Answers
Answer:
i think it is 5/12???
I hope i am right :C, if not you can delete this answer
plz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need helpplz help i need help
Answers
Answer:
the answer should be 9
Step-by-step explanation:
\((256 * 3^{-5} * 6^{0} )^{-2} * (\frac{3^{-2}}{2^{3}} )^{4} * 2^{28}\)
\((256*\frac{1}{3^{5}} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((256*\frac{1}{243} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{256}{243} *6^{0})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{256}{243})^{-2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\((\frac{243}{256})^{2}*(\frac{3^{-2}}{2^{3}})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{2^{3}*3^{2}})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{8*9})^{4}*2^{28}\)
\(\frac{59049}{65536}*(\frac{1}{72})^{4}*2^{28}\)
\(\frac{59049}{65536}*\frac{1}{26873856}*2^{28}\)
\(\frac{9}{65536}*\frac{1}{4096}*2^{28}\)
\(\frac{9}{65536*4096}*2^{28}\)
\(\frac{9}{268435456}*268435456\)
\(9\)
Answer:
the answer should be 9
Step-by-step explanation:
please mark me brainliest thanks so much i really appreciate it!
hope you have an amazing rest of your day and thanks for your time!
what is the area of this figure pleas ill give brainy and lots of points
Answers
The purchase price of a camcorder is $818 what is the total price if the sales tax rate is 8.5%
Answers
Last week,Barry's Swimwear sold/15 of its bathing suits in stock .Philip's Sun Wear sold 5 out of 72 of its bathing suits in stock. Which store sold a greater fraction of the bathing suits in stock?
Answers
Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.
Step-by-step explanation:
Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.
To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.
Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.