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A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
- a)16 = (1.02)x/4
- b)2 = (1.02)x
- c)16 = (1.08)4x
- d)2 = (1.02)x/4
- e)1/16 = (1.02)4x
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A certain investment grows at an annual interest rate of 8%, compounde...
Compound interest is computed using the following formula:
F = P ( 1 + r/n)nt, where
F = Final value
P = Principal
r = annual interest rate
n = number of compounding periods per year
t = number of years
F = Final value
P = Principal
r = annual interest rate
n = number of compounding periods per year
t = number of years
From the question, we can deduce the following information about the growth during this period:
At the end of the x years, the final value, F, will be equal to 16 times the principal (the money is growing by a factor of 16).
Therefore, F = 16P.
r = .08 (8% annual interest rate)
n = 4 (compounded quarterly)
t = x (the question is asking us to express the time in terms of x number of years)
Therefore, F = 16P.
r = .08 (8% annual interest rate)
n = 4 (compounded quarterly)
t = x (the question is asking us to express the time in terms of x number of years)
We can write the equation
16P = P (1 + .08/4)4x
16 = (1.02)4x
16P = P (1 + .08/4)4x
16 = (1.02)4x
Now we can take the fourth root of both sides of the equation. (i.e.the equivalent of taking the square root twice) We will only consider the positive root because a negative 2 doesn't make sense here.
161/4 = [(1.02)4x]1/4
2 = (1.02)x
161/4 = [(1.02)4x]1/4
2 = (1.02)x
The correct answer is B.
Most Upvoted Answer
A certain investment grows at an annual interest rate of 8%, compounde...
Introduction:
The given investment grows at an annual interest rate of 8% compounded quarterly. We need to find the equation that can be solved to determine the number of years it would take for the investment to increase by a factor of 16.
Understanding Compound Interest:
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the interest is compounded quarterly, so n = 4.
Approach:
To find the equation that can be solved for the number of years, we need to set up the equation using the given information.
Solution:
Let's analyze each option and see which one fits our requirements:
a) 16 = (1.02)^(x/4)
This equation does not have the factor of 16 on the right side, so it cannot be solved to find the number of years.
b) 2 = (1.02)^x
This equation has the factor of 16 on the right side (2^4 = 16), so it can be solved to find the number of years.
c) 16 = (1.08)^(4x)
This equation has the interest rate of 8% compounded annually, which does not match the given information. Therefore, it cannot be solved to find the number of years.
d) 2 = (1.02)^(x/4)
This equation does not have the factor of 16 on the right side, so it cannot be solved to find the number of years.
e) 1/16 = (1.02)^(4x)
This equation has the factor of 16 on the left side (1/16 = (1/2)^4), but it does not match the given interest rate of 8% compounded quarterly. Therefore, it cannot be solved to find the number of years.
Conclusion:
Out of the given options, only option b) 2 = (1.02)^x fits the requirements and can be solved to find the number of years it would take for the investment to increase by a factor of 16.
The given investment grows at an annual interest rate of 8% compounded quarterly. We need to find the equation that can be solved to determine the number of years it would take for the investment to increase by a factor of 16.
Understanding Compound Interest:
Compound interest is calculated using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the interest is compounded quarterly, so n = 4.
Approach:
To find the equation that can be solved for the number of years, we need to set up the equation using the given information.
Solution:
Let's analyze each option and see which one fits our requirements:
a) 16 = (1.02)^(x/4)
This equation does not have the factor of 16 on the right side, so it cannot be solved to find the number of years.
b) 2 = (1.02)^x
This equation has the factor of 16 on the right side (2^4 = 16), so it can be solved to find the number of years.
c) 16 = (1.08)^(4x)
This equation has the interest rate of 8% compounded annually, which does not match the given information. Therefore, it cannot be solved to find the number of years.
d) 2 = (1.02)^(x/4)
This equation does not have the factor of 16 on the right side, so it cannot be solved to find the number of years.
e) 1/16 = (1.02)^(4x)
This equation has the factor of 16 on the left side (1/16 = (1/2)^4), but it does not match the given interest rate of 8% compounded quarterly. Therefore, it cannot be solved to find the number of years.
Conclusion:
Out of the given options, only option b) 2 = (1.02)^x fits the requirements and can be solved to find the number of years it would take for the investment to increase by a factor of 16.
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A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer?.
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?a)16 = (1.02)x/4b)2 = (1.02)xc)16 = (1.08)4xd)2 = (1.02)x/4e)1/16 = (1.02)4xCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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