Aria invested $96,000 in an account paying an interest rate of 1.8% compounded
monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest tenth of a year, for the value of the account to reach $113,300?
Answers
Answer:
9.2
Step-by-step explanation:
On a principle of $96,000.00, with an interest rate of 1.8% per year and compounded 12 times each year, it will take 9.212 years to accumulate a total of $113,300.00 with compounded interest.
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n\()^{nt}\),
where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
Aria invested $96,000 in an account paying an interest rate of 1.8% compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 1.8/100
r = 0.018 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(113,300.00/96,000.00) / (12 × [ln(1 + 0.018/12)])
t = ln(113,300.00/96,000.00) / (12 × [ln(1 + 0.0015)])
t = 9.212 years
t = 9.2 years to the nearest tenth.
Therefore, the required time is 9.2 years to the nearest tenth.
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Related Questions
Answer the question with an algebraic expression.
The perimeter of a square is m meters. How long, in centimeters, is each side of the square?
Answers
The length of the square in centimetres in algebraic expression is 25m
How to find the side length of a square?The perimeter of a square is m meters.
The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:
Therefore,
perimeter of a square = 4l
where
l = side lengthTherefore,
m = 4l
where
m = perimeter of the squarel = m / 4 meters.
Therefore, the side length of the square in centimetres is as follows:
1 meters = 100 cm
m / 4 meters = ?
cross multiply
length of the square in meters = m / 4 × 100
length of the square in meters = 100m / 4
length of the square in meters = 25m
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2/3 es equivalente a 4/5?
Answers
we can conclude that 2/3 is not equal to 4/5.
To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.
To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.
For 2/3 and 4/5, we have:
2 * 5 = 10
3 * 4 = 12
Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.
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This figure represents a garden box that is to be filled with soil.
How much soil will it take to fill the garden box?
Enter your answer in the box.
ft³
Three-dimensional figure that could be formed by placing a smaller rectangular prism on top of a larger rectangular prism such that the widths of the prisms are the same. The larger bottom prism has a length of 19 feet, a width of 12 feet, and a height of 6 feet. The smaller top prism has a length of 10 feet and a height of 3 feet.
Answers
Answer:
1134 ft^3
Step-by-step explanation:
Help me please.......
Answers
Answer:
decompose
numerator
mixed number
Step-by-step explanation:
1. To DECOMPOSE is to break apart a number.
e.g. to decompose 853: 800 + 50 + 3
2. The NUMERATOR is the top number in a fraction (the bottom number is the denominator).
3. A number that has whole number part and fraction part is a MIXED NUMBER, e.g. \(6\frac23\)
which diagram below appears to show a pair of perpendicular lines Diagram A Diagram B Diagram C. Explain your Answer.
Answers
The answer for it is diagram B because it does not cross or have parallel lines
Oscar Lieberman needed to borrow money from his bank to remodel his home. To get the loan, he gave the bank nod 120-day note for $32,500, dated April bearing exact interest 12 1/2%
A. The note came due for for payment on what date?
B. Oscar paid the note on it’s due date by giving the bank a check for what amount?
Answers
Calculator Triangle ABC is similar totriangle DEF. The length of AC is 12 cm. The length of EF is 35 cm. The length of DF is 20 cm What is the length of BC ? Enter your answer in the box. cm
Answers
Answer:
BC = 21 cm
Step-by-step explanation:
In similar triangles the corresponding sides are in same proportion.
Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.
\(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)
\(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)
318÷53 with a remainder
Answers
Answer:
6
Step-by-step explanation:
318 / 53 = 6
the remainder is 0
Deshawn says that the ratios 3:5 and 5:7 are equivalent ratios because by adding 2 to both terms of 3:5 you get 5:7. Is Deshawn correct? Explain
Answers
Answer:
False
Step-by-step explanation:
3:5 and 5:7 can also be written as 3/5 and 5/7 and 3/5≠5/7
Answer:
no
Step-by-step explanation:
3:5 and 5:7 can also be written as 3/5 and 5/7
which expression is equivalent to 5x +2-x10
Answers
Answer:
x= 30
Step-by-step explanation:
3+2-1441+x= 30
Answer: 5x+2-x10= 30
HELP PLS
In the function n = p(m), the __________ is all the possible values of m, and the __________ is all the possible values of n
Answers
Answer:
420
Step-by-step explanation:
420 69
What is the slope of a line that is perpendicular to the line represented by the equation x – y = 8? 1 −1 8
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
\(x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}\)
Subtract using a number line.
1.4−1.7
Plot the minuend and the difference on the number line.
Answers
The difference between the numbers 1.4 and 1.7 is -0.3 after using the number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
As we can see in the number line:
1.4 < 1.7
If we take the difference between these two numbers
From the number line:
= 1.4 - 1.7
= -0.3
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After using the arithmetic operation concept:
The difference between the numbers:
= 1.4 - 1.7
= -0.3
Thus, the difference between the numbers 1.4 and 1.7 is -0.3 after using the number line.
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lve for m.
-3 + m
9 = 10
A.
-30
B.
63
C.
87
D.
93
Answers
The value of m that satisfies the equation -3 + m = 9 is m = 12.
To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.
-3 + m = 9
To move -3 to the other side, we can add 3 to both sides of the equation:
-3 + 3 + m = 9 + 3
Simplifying, we have:
m = 12
Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.
None of the provided answer options (A, B, C, D) match the correct solution.
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a gift box is shaped of a right rectangle prism
Answers
Four less than the product of 8 and a number equals 6
Answers
Answer:
8a - 4 = 6
Brainiest Pls
Answer:
a=1 1/4
Step-by-step explanation:
8a-4=6
8a=10
a=10/8
a=5/4
a=1 1/4
J.D. Power and Associates conducts vehicle quality surveys to provide automobile manufacturers with consumer satisfaction information about their products (Vehicle Quality Survey, January 2010 ). Using a sample of vehicle owners from recent vehicle purchase records, the survey asks the owners a variety of questions about their new vehicles, such as those shown below. For each question, state whether the data collected are categorical or quantitative and indicate the measurement scale being used.
a. What price did you pay for the vehicle?
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
d. What is the current mileage?
e. What is your overall rating of your new vehicle? A 110 -point scale, ranging from I for
unacceptable to 10 for truly exceptional, was used.
Answers
Answer:
Categorical data includes
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Quantitative data includes
a. What price did you pay for the vehicle?
d. What is the current mileage?
Step-by-step explanation:
Categorical data refers to the kind of data in which the variables are grouped based on a particular quality, ticking a particular box or satisfying some specific requirements.
It uses one or more qualitative property/properties to assign variables into a limited, usually fixed groups or categories. Note that the qualitative property might be a grouped data of numerical values. As long as there are easily separable and recognizable groups, it is categorical data.
This is also called qualitative data.
Quantitative data is a data that is strictly about numerical values. A dataset that consists of numerical values of the members of the dataset. Deals almost exclusively with numbers, usually ungrouped.
So, examining the given datasets one at a time
a. What price did you pay for the vehicle?
The answer to this question is a numerical value and for various customers, it builds up a dataset of strictly numerical values. Hence, this resulting data is a quantitative data.
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
The answers to this question can only take 3 forms; Cash, Lease or Finance, indicating that all the variables in the dataset can only take on limited, fixed number of groups/categories. Hence, this dataset is a categorical data.
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
The answers to this question too can take on 4 limited, fixed categories or groups, Hence, it's easy to see that this dataset is also categorical data.
d. What is the current mileage?
The answer to this question is a numerical value. Various answers from numerous persons would lead to a data of numbers. Hence, this is a quantitative data.
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Limited, fixed categories or groups (10 groups) are also available for this data, hence, it is easily a categorical data.
Hope this Helps!!!
(-100)/(-5)=
Help me with both questions please and thank you
Answers
Answer:20
That's the answer!
Step-by-step explanation:
-100/-5
=20
Which of the following is a Rational Number? √11 √14 √77 15
Answers
Answer:
1/2
Step-by-step explanation:
Using the Binomial distribution,
If n=10 and p=0.3, find P(x=4)
Answers
Answer:
P(x=4)
Step-by-step explanation:
0.3(10=4)
what is the question. Wrong question asked.
Alex conduct an experiment with a spinner he recorded the frequency of each spin landing on letters A through D in the table. based on the data in the table what is the experimental probability that the next spin will land on letter B? A. 4/15 B. 1/5 C. 1/4 D. 3/10
Answers
Answer
3/10
Step-by-step explanation:
what is 10% of 22 million dollars
if you know how to do this too pls help but its ok if you just know the top question^^
also if you know it, can you 10% of that 7 times. basically my question is On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? Round to the nearest million.
27 million
35 million
37 million
38 million
Answers
Answer:
38 million
Step-by-step explanation:
Use the hundredth grids to answer the question.
Which equation is shown by the model?
See picture below
Answers
Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).
How to identify the correct equation?To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.
In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.
On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:
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the park manager wants to make a timetable for buses and mini buses leaving the park at different times of the day, from 8:00am to 5:00pm Buses andmini_buses leave the park atintervals of 40minutes and 50 minutes respectively after loading . Both vehicles start loading at the same time.
help the park manager to;
(a) draw a departure time table for the two vehicles from 08:00am to 5:00pm
(b) Identify any time of the day when the two vehicles will leave the park at the same time.
Answers
a) Departure tabIe is mentioned beIοw.
b) The twο vehicIes wiII Ieave the park at the same time at 8:00am, 10:20am, 12:40pm, and 3:00pm.
What is Ieast cοmmοn muItipIe?
Least Cοmmοn MuItipIe (LCM) In Mathematics, the LCM οf any twο is the vaIue that is evenIy divisibIe by the twο given numbers. The fuII fοrm οf LCM is Least Cοmmοn MuItipIe. It is aIsο caIIed the Least Cοmmοn Divisοr (LCD).
a) Tο draw the departure time tabIe, we can start by Iisting the departure times fοr the buses and mini buses separateIy.
Fοr the buses:
First departure: 8:00am
Subsequent departures: 8:40am, 9:20am, 10:00am, 10:40am, 11:20am, 12:00pm, 12:40pm, 1:20pm, 2:00pm, 2:40pm, 3:20pm, 4:00pm, 4:40pm
Fοr the mini buses:
First departure: 8:00am
Subsequent departures: 8:50am, 9:40am, 10:30am, 11:20am, 12:10pm, 1:00pm, 1:50pm, 2:40pm, 3:30pm, 4:20pm
We can then cοmbine the twο Iists tο create the departure time tabIe:
Departure Time TabIe:
8:00am - Bus, Mini Bus
8:40am - Bus
8:50am - Mini Bus
9:20am - Bus
9:40am - Mini Bus
10:00am - Bus
10:30am - Mini Bus
10:40am - Bus
11:20am - Bus, Mini Bus
12:00pm - Bus
12:10pm - Mini Bus
12:40pm - Bus
1:00pm - Mini Bus
1:20pm - Bus
1:50pm - Mini Bus
2:00pm - Bus
2:40pm - Bus, Mini Bus
3:20pm - Bus
3:30pm - Mini Bus
4:00pm - Bus
4:20pm - Mini Bus
4:40pm - Bus
5:00pm - (Nο departures)
b) Tο identify any time οf the day when the twο vehicIes wiII Ieave the park at the same time, we need tο find the intersectiοn οf the departure times fοr the buses and mini buses. One way tο dο this is tο Iist the departure times fοr each vehicIe in terms οf minutes past 8:00am, and then find a cοmmοn muItipIe οf the twο intervaIs.
Fοr the buses:
First departure: 0 minutes (8:00am)
Subsequent departures: 40 minutes, 80 minutes, 120 minutes, 160 minutes, 200 minutes, 240 minutes, 280 minutes, 320 minutes, 360 minutes, 400 minutes, 440 minutes, 480 minutes, 520 minutes, 560 minutes
Fοr the mini buses:
First departure: 0 minutes (8:00am)
Subsequent departures: 50 minutes, 100 minutes, 150 minutes, 200 minutes, 250 minutes, 300 minutes, 350 minutes, 400 minutes, 450 minutes, 500 minutes, 550 minutes
The Ieast cοmmοn muItipIe (LCM) οf 40 and 50 is 200, sο we can find the departure times fοr bοth vehicIes at every 200-minute intervaI:
At 8:00am (0 minutes), bοth vehicIes depart
At 10:20am (200 minutes), bοth vehicIes depart
At 12:40pm (400 minutes), bοth vehicIes depart
At 3:00pm (600 minutes), bοth vehicIes depart
Therefore, the two vehicles will leave the park at the same time at 8:00am, 10:20am, 12:40pm, and 3:00pm.
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Write a recursive sequence that represents the sequence defined by the following explicit formula:
Answers
The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:
\(a_1 = -32\)\(a_{n + 1} = -\frac{1}{4}a_n\)What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
The first term and the common ratio for this problem is given as follows:
\(a_1 = -32, q = -\frac{1}{4}\)
The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:
\(a_{n + 1} = -\frac{1}{4}a_n\)
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-4x =14 please explane
Answers
Answer:
x=-3.5
Step-by-step explanation:
14/-4 = -3.5
Answer:
If you're asking how -4x could equal 14, here's how:
Substitute -3.4 for x, so -4x-3.5, which would equal 14.
In which situation would the quotient of -24 ÷ 3 be used to answer the question?
A. The temperature of a substance decreased by 24°C per minute for 3 minutes. What was the overall change of the temperature of the substance?
B. A football team lost 24 yards on one play, then gained 3 yards on the next play. How many total yards did the team gain on the two plays?
C. Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day?
D. A cookie jar contains 24 cookies. Each child receives 3 cookies. How many children are there?
Answers
Answer:
C
Step-by-step explanation:
Covert 3/7 into percent
Answers
The percentage of fraction 3/7 is 42.8571%.
what is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given fraction:
3/7
To convert the fraction into percentage we have multiply 100
3/7*100
=300/7
= 42.8571%
Hence, the percentage of fraction 3/7 is 42.8571%.
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A shop makes a profit of £2 750 in March
It has an Easter sale and the profit for April is £3 162.50
Work out the profit percentage increase
Answers
The percent increase of the profit is 15%
How to determine the percent increase of the profit?In this question, the figures are given as
Profit in March = £2750
Profit in April = £3162.50
The percentage of the increase of the profit is then calculated using the following equation
Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%
Substitute the known values in the above equation, so, we have the following representation
Increase percentage = (3162.50 - 2750)/2750 * 100%
Evaluate
Increase percentage = 15%
Hence, the increase in percentage is 15%
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Factor: x^6-5x^4-5+x
Answers
The value of the given expression x^6 -5x^4 - 5 + x simplified as; x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as ;
Factor: \(x^6 -5x^4 - 5 + x\)
From the given expression, we have
\(x^6 -5x^4 - 5 + x\)
Group the expression in two part;
So, we have;
\(x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)\)
Now Factorize each group of the expression;
\(x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)\)
The given expression cannot be further simplified.
Hence, the value of \(x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)\)
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