Answer:
$313.98
Step-by-step explanation:
[tex]Equation: A=P(1+\frac{r}{n} )^{nt} \\\\A=12000(1+\frac{0.0375}{12} )^{12(5.5)} \\\\A=12000(1+0.003125)^{66} \\\\A=12000(1.003125)^{66}\\\\A=12000(1.228665)\\\\A=14743.98\\[/tex]
So to see the difference of account balances we would subtract offer 1 balance from offer 2 balance.
14743.98-14430 = 313.98
So, therefore the difference in the account balances at the end of the loan terms is $313.98.
Note: the 5.5 comes from converting 66 months to years which is 5.5
A group of students were asked which club they planned to join.
Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2
Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).
The statement that is true about the probabilities is;
B: The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
How to interpret the probabilities?We are given the various students club and their probabilities of being randomly selected;
Garden club = 0.1
Robotics club = 0.2
Technology club = 0.5
Zoology Club = 0.2
Now, it is clear that Technology cub has the highest probability of being selected at 0.5 while Garden club has the least probability of being selected.
However we see that Robotics club and zoology club have the same probability and as such looking at the options, only option B is true.
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(6x ^ 3 - x ^ 2 - 14x + 5):(2x - 1)
The final result of algebra is: (6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)This is the simplified form of the given expression.
What is simplification?Simplification is the process of making an expression or equation simpler and easier to understand or work with. In mathematics, simplification often involves combining like terms, removing unnecessary operations, or reducing the number of terms in an expression. The goal of simplification is to obtain an equivalent expression that is clearer, more manageable, and easier to interpret.
Here ,
is the step by step process:
(6x ^ 3 - x ^ 2 - 14x + 5):(2x - 1)
Step 1: Divide 6x^3 by 2x and write the quotient 3x^2.
Step 2: Multiply the denominator (2x - 1) by the quotient (3x^2)
Step 3: Subtract the result from the numerator and bring down the next term of the numerator ( x^2)
Step 4: Repeat the process by dividing the x^2 by 2x and write the quotient -x.
Step 5: Multiply the denominator (2x - 1) by the quotient (-x)
Step 6: Subtract the result from the numerator and bring down the next term of the numerator ( -14x)
Step 7: Repeat the process by dividing the -14x by 2x and write the quotient -7
Step 8: Multiply the denominator (2x - 1) by the quotient (-7)
Step 9: Subtract the result from the numerator and bring down the next term of the numerator (5)
Step 10: We can see that the degree of the remainder is less than the degree of the denominator so we can write the remainder as 5/(2x-1)
So the final result is:(6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)
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3. An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river. Write an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch.
Answer:
the equation for the ellipse that describes the arch is:
(x^2/20^2) + (y^2/6^2) = 1
Step-by-step explanation:
An ellipse can be represented by the equation (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. In this case, the x-axis coincides with the water level and the y-axis passes through the center of the arch, so the center of the ellipse is at the point (0, 6).
For the arch in question, the semi-major axis is 20 meters (since the arch spans a river 20 meters wide) and the semi-minor axis is 6 meters (since the center of the arch is 6 meters above the center of the river).
So the equation for the ellipse that describes the arch is:
(x^2/20^2) + (y^2/6^2) = 1
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain.
In the currency pair USD/CAN, USD is the
O A. pegged currency
OB. quote currency
OC. reserve currency
OD. base currency
Answer: D. base currency
Step-by-step explanation: In the foreign exchange market, currencies are traded in pairs. A currency pair consists of two currencies, with one currency being quoted against the other.
In a currency pair, the base currency is the first currency listed. It is the currency against which the exchange rate is quoted. In the case of USD/CAN, USD is the base currency. The base currency serves as a reference point for calculating exchange rates. It helps determine the value of the quote currency which is the second currency listed in a currency pair. It represents the value of the quote currency needed to purchase one unit of the base currency.
Furthermore, changes in the exchange rate reflect the strength or weakness of the base currency relative to the quote currency.
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Michelle is facing west and rebeca is facing northeast. They both make half a turn to their left. What do they need so they both face north.
A. Michelle makes a quarter turn to her left and Rebecca makes three eight turn to her right.
B. Michelle makes a quarter turn to her right and rebecca makes three eight turn to her right.
C. Michelle makes a quarter turn to her her left and rebecca makes a three eight turn to her left.
D. Michelle makes a quarter turn to her right and Rebecca makes a three eight turn to her left.
The correct answer is Michelle makes a quarter turn to her right and Rebecca makes a three eight turn to her left.
What is speed?Speed is the rate of change of position. It is the physical quantity that measures how quickly an object moves from one place to another. It is measured in units such as meters per second, kilometers per hour, or miles per hour. Speed is related to velocity, which is the measurement of how quickly an object moves in a specific direction. Speed is an important concept in physics and is necessary for understanding how the universe works.
Michelle makes a quarter turn to her right and Rebecca makes a three eight turn to her left. By making these turns, they will both end up facing north. A quarter turn to the right is the same as a three eight turn to the left. This is because a full turn is 360 degrees, so a quarter turn is 90 degrees and a three eight turn is also 90 degrees.
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PLEASE HELP RADIUS I THINKEASTY!!
The approximate distance around the circular field is 172.7 feet.
How to find the distance around a circle?A diagram of a roundabout is being designed to improve driver safety on a busy road. The radius of the circular field planned for landscaping is 27.5 feet.
Therefore, the approximate distance around the outside of the circle can be calculated as follows:
The distance around the circle is the circumference of the circle.
Hence,
circumference of a circle = 2πr
where
r = radiusTherefore,
distance around the circle = 2 × 3.14 × 27.5
distance around the circle = 172.7 feet
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Consider the circle given by the equation (x – 2)2
+ (y + 1) 2
= 5. Find the center and radius.
The center and the radius of the circle (x – 2)²+ (y + 1)² = 5 are
(2, -1) and √5, respectively.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
The equation of the circle,
(x – 2)²+ (y + 1)² = 5.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Comparing the equations, we get,
h = 2 and k = -1 and r = √5
That means,
the center = (2, -1) and the radius = √5
Therefore, the center = (2, -1) and the radius = √5.
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TOP Electronics is a small business with five employees. The mean (average) weekly salary for the five
employees is $360. If the weekly salaries of four of the employees are $340, $340, $345, and $425, what is
the salary of the fifth employee?
The answer is $350
How to find the Median?By ranking the wages of a group of employees in descending order, you may determine the median base salary by finding the wage that is in the Middle of the distribution . 50 percent of earnings fall below the median, while 50 percent of salaries rise above the median.
ExplanationThe average of a set of numbers is known as the mean. If there are five salaries involved and the mean is $360, the total can be calculated by
Average = Total / number
Total = (Average)(Number)
Total = $360 * 5 = $1800
Four of the wages are spoken for, so we add them up and take $1800 out of the equation to get our result.
so $340 + $340 + $345 + $425 = $1450
and $1800 - $1450 = $350
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A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They write a total of 46 songs.
How many songs did the guitarist write? How many songs the drummer write?
The number of songs written by the guitarist and by the drummer is given as follows:
Guitarist: 28.Drummer: 18.How to obtain the number of songs written by each?The number of songs written by each is obtained using a system of equations, for which the variables are given as follows:
Variable x: number of songs written by the guitarist.Variable y: number of songs written by the drummer.The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote, hence:
x = 2y - 8.
They wrote a total of 46 songs, hence:
x + y = 46.
Replacing the first equation into the second, the number of songs written by the drummer is of:
2y - 8 + y = 46
3y = 54
y = 18.
Hence the number of songs written by the guitarist is given as follows:
x = 46 - 18
x = 28.
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A foreigner buys some typical Nepali goods in Kathmandu After allowing 10% discount and then adding 15% VAT, be pays Rs.4140. Find marked price of goods. How much does he get while leaving Nepal?
Market price of goods is 3942.86 Rs.
What is market price?The price at which a goods, assets, instruments or raw materials are bought and sold at a wholesale market.
What is the market price of the goods?
let, market price of Nepali goods = X
after allowing discount and vat the price of goods = 4140 Rs
discount = 10 %
the amount of discount = X 10/ 100
Vat added = 15%
the amount of vat added = X 15/ 100
Now, discount is subtracted from market price and vat is added to it.
The equation will be
X - X10/100 + X15/100 = 4140 Rs
X = 3942.86 Rs
market price of goods = 3942.86 Rs
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Which quadratic inequality does the graph below represent?
5
4
O yzx²-3
O y≤x²+3
O y≤x²-3
Ov> ²13
32
3-
2-
4
3-5-4-3-2-1 1
2 3
Therefore , the solution to the given problem of quadratic equation comes out to be real.
An explanation of a quadratic equation.The quadratic equation x ax2+bx+c=0 is a non - linear regression model in a single variable. a 0. According to the First Theorem of Algebra, this polynomial has at least single solution because it is of second order. There could be simple or complex solutions. A four-variable equation is referred to as a quadratic equation. This implies that it must have at least one squared word. A typical formula for resolving quadratic formula is "ax2 + bx + c = 0," where the numerical factors or constant a, b, and c stand in for the undefined variable "X."
Here,
The graph is shown.
For this graph, we must discover the inequality.
The parent role is:
f(x) = x²
When we move the parent function back three units, we get,
f(x) = x² - 3
It is evident from this that option B is incorrect.
Check the additional disparities we obtain now.
Using the 1 and 3 choices we receive, choose any location from the shaded area.
x=-2 and y=0 are entered one by one into the inequality to yield,
FIRST CHOICE
y >= x²-3
0 >= (-2)²-3
0 >= 4-3
0>= 1
That is untrue.
3rd option
y<= x² - 3
0<= (-2)² -3
0<=1
This is real.
Choice 3 is the right one, thus.
Therefore , the solution to the given problem of quadratic equation comes out to be real.
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Kevin has six and one fourth feet of wood. he is making birdhouses and trimming the door of each house in wood. if he needs one half foot for each birdhouse, how many birdhouses can he make with the wood he has??
When he has six and one-fourth feet of wood and one-half foot is needed for each birdhouse, he can create 12 birdhouses out of it.
what is unitary method ?Simply put, the unit technique is used to extract a single unit value from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.
given
Kevin has six and one fourth feet of wood = 6 + 1/4 = 25/4
one half foot for each birdhouse = 1/2
so number of birdhouses = 25/4 / 1/2 = 25/2
When he has six and one-fourth feet of wood and one-half foot is needed for each birdhouse, he can create 12 birdhouses out of it.
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The pharmacist has a 4.3 L bottle of cough syrup. If she fills a bottle that is 1,900 ml, how many ml of cough syrup does the pharmacist have left? (1 L = 1,000 ml)
240 ml
2,400 ml
3,100 ml
6,200 ml
The total volume of cough syrup that the pharmacist will have left would be = 2,400ml. That is option B.
Who is a pharmacist?A pharmacist is an individual that is trained and licensed to dispense prescribed medication to individuals in the correct proportion.
The volume of the cough syrup the pharmacist has = 4.3L
But 1 L = 1000 ml
4.3 L = 4.3 × 1000 = 4300ml
The quantity of syrup transferred to a bottle = 1,900 ml
Therefore the amount remaining = 4300 - 1900 = 2,400ml.
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What type of variable is required to construct a confidence interval for a population proportion? Choose the correct answer below O A. Quantitative O B. Qualitative with any number of possible outcomes O C. Continuous D. Qualitative with 2 possible outcomes O E. Discrete O F. Qualitative with 3 or more possible outcomes
Qualitative with 2 possible outcomes of variable is required to construct a confidence interval for a population proportion.
The goal of qualitative research is to collect and analyze non-numerical (descriptive) data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality. In-depth interviews, focus groups, or observations are frequently used in this kind of study to gather the information that is rich in context and detail.
To investigate complicated phenomena or to learn more about people's viewpoints and experiences on a certain subject, qualitative research is frequently used. It is especially helpful for academics who wish to comprehend the meaning that individuals attribute to their experiences or who want to identify the fundamental causes of people's conduct. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches.
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(-3) = -1 B. h(8) = 21 C. h(13) = 18 D. h(2) = 16
Answer:
The question is incomplete, but if I had to guess, it's an exercise in using the intermediate value theorem. The IVT says that for a continuous function , there is some value of within any interval , i.e. , in the domain of such that when , or when .We're told that and . The IVT then guarantees the existence of some value of between -2 and 8 such that .It looks like is one of several possible answer choices. We can't say anything about the value of because we only know how behaves between -2 and 8; the number 13 falls outside of this range. So this choice is not correct.
Step-by-step explanation:
pls mark as brainliest
Do you guy know what is 4/5 - 3/8 for my little cosin
Answer:
17/40
Step-by-step explanation:
4/5-3/8
32/40-15/40
17/40
NEED HELP PLS ASAP AND THX PIC IS ATTACHED
If f(x)=5x-1 and g(x) =2x^2+1 what is the value of (fxg)(-3)?
The value of (fxg)(-3) if f(x)=5x-1 and g(x) =2x^2+1 will be 94.
What is a function?A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B. It is a relation “f” in which each element of set “A” is mapped with only one element belonging to set “B”. Also in a function, there can’t be two pairs with the same first element.
f(x)=5x-1
g(x) =2x^2+1
fxg = 5(2x^2+1) - 1
fxg = 10x^2 + 5 - 1
fxg = 10x^2 + 4
fxg(-3) = 10(-3)^2 + 4
fxg(-3) = 10(9) + 4
fxg(-3) = 90 + 4
fxg(-3) = 94
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The graph shows a proportional relationship between time and number of boxes a machine packages. How many boxes does the machine package in 5 minutes?
In linear equation, 300 boxes does the machine package in 5 minutes .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
In 5 minutes the machine package does
= 5*60
= 300 boxes.
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A secretary listed the frequency of calls by a patient to a doctor's office during a year, and the data is displayed in the histogram.
A histogram titled Calls To A Doctor. The x-axis is labeled Number of Calls and has intervals listed for 1 to 25, 26 to 50, 51 to 75, and 76 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every five units up to 60. There is a shaded bar for 1 to 25 that stops at 58, for 26 to 50 that stops at 34, for 51 to 75 that stops at 17, and for 76 to 100 that stops at 12.
Which of the following best describes the spread and distribution of the data?
The data is skewed to the higher values because many patients call the doctor several times a day when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The data is bimodal with a narrow spread because many patients call the doctor several times a day when they are sick.
The data is normal and has a wide spread because many patients only call the doctor once or twice a year when they are sick.
Due to the fact that many people only call their doctors when they are ill once or twice a year, the data is skewed toward the lower levels.
What is meant by histogram?A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. Each column's data count or percentage of occurrences are shown on the vertical y-axis. Data distribution patterns can be seen visually using columns.
A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.
Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values).
Therefore, the correct answer is option b) The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
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ignore the text just answer the question please ty <3
Answer: 53.6 degrees Farenheit
Step-by-step explanation:
The question says that the temperature in Washington was 12 degrees Celsius.
To convert that into Fahrenheit, plug in the value 12 in the equation given.
F = 1.8*12+32
= 53.6
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A drink stand is selling small drinks for $2 each and large drinks for $4 each. One day, a total of 150 drinks were sold for $552. How many large drinks were sold?
Part A: Define your variables
Part B: Write two equations for this scenario
Part C: determine how many large drinks were sold
Using equation, the number of large drinks is 126.
How to find the number of large drinks sold?A drink stand is selling small drinks for $2 each and large drinks for $4 each. One day, a total of 150 drinks were sold for $552.
The number of large drinks sold can be calculated as follows:
Using equation,
let
x = number of small drinks
y = number of large drinks
Hence,
2x + 4y = 552
x + y = 150
multiply equation(ii) by 2
2x + 4y = 552
2x + 2y = 300
subtract equation(ii) from equation(i)
2y = 252
divide both sides by 2
y = 252 / 2
y = 126
Therefore,
number of large drinks = 126
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Help me please!!!!!!
Answer:
a
Step-by-step explanation:
simplify
2/9 to the power of 2
[tex](\dfrac{2}{9} )^2[/tex]
Can be written as:
[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]
To multiply two fractions, you need to multiply the numerator by the numerator and multiply the denominator over the denominator.
Multiply:
[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]
[tex]\dfrac{2\times2}{9\times9}[/tex]
[tex]=\fbox{$\dfrac{4}{81} $}[/tex]
Two functions are shown below. Which function has a greater rate of change
Answer: Function B
Step-by-step explanation: Function A's equation would be y = x + 3 and although they have a greater y-intercept (starting point on x) the rate of change is less than Function B.
In Nepal, some students paddle a kayak to get to school. Suppose it takes one student 1/4 hour to paddle 1/2 mile How far would the student paddle in `t` hours at this speed?
what is t
The distance that the student can travel in "t" hours if the speed is constant is:
distance = (2 mi/h)*t
How far would the student paddle in `t` hours at this speed?
Here we need to remember the relation between time, distance, and speed:
distance = time*speed.
Solving for speed, we will get:
Speed = distance/time
Here, we know that the student can travel 1/2 of a mile in 1/4 of an hour, then we have:
distance = 1/2 of a miletime = 1/4 of an hour.With that, we can find the speed:
speed = (1/2 of a mile)/(1/4 of an hour) = 2 miles per hour.
Then the distance that the student can paddle in "t" hours is written as:
distance = (2 mi/h)*t
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Which expressions are equivalent to 7(-x-3)? Select two options.
0-5-x-21
0-7-x-7(3)
06x-21
06-x-4
07(-x)-7(3)
Answer:
07(-x)-7(3)
Step-by-step explanation:
7(-x-3)
-7x-21
07(-x)-7(3)
-7x-21
Sam ordered a $4.90 meal the tax rate was 7% .he paid with a $10 bill how much should he get back
Answer:
$4.76
Step-by-step explanation:
7% x 4.90 = 0.34
4.90 + 0.34 = 5.24
10 - 5.24 = 4.76
To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.
The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
What is simple interest?
Simple interest is based on the principal amount of a loan or the first deposit in a savings account. Simple interest doesn't compound, which means a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.
The simple interest earned can be calculated by using this formula
A = P(1 + rt)
Where,
A is the future value.
P is the principal value.
r is the interest rate.
t is the time.
Now Substituting the values into the formula, we have,
A = 16,000[1 + (0.08 × 3)]
A = 16,000[1 + 0.24]
A = 16,000× 1.24
Future value, A = $19,840.
Following that, we will compute the monthly payment over a 36-month period as follows:
Monthly payment = Future value/Time
Monthly payment = 19,840/36
Monthly payment = $551.11
Similarly, we will compute the credit card's compound interest:
A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾
A = 16000[1 + 0.025]⁸⁴
A = 16000× 1.025⁸⁴
A = 9000 × 3.49258954
Future value, A = $45425.80
Following that, we will compute the monthly payment over an 84-month period as follows;
Monthly payment = Future value/Time
Monthly payment = 45425.80/84
Monthly payment = $540.78.
Hence, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
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