CA Foundation Exam > CA Foundation Questions > Which of the following is false?a)The longer ...
Start Learning for Free
Which of the following is false?
- a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.
- b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.
- c)A future dollar is always less valuable than a dollar today if interest rates are positive.
- d)The discount factor is the reciprocal of the compound factor.
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Which of the following is false?a)The longer the time period, the smal...
False Statement
Option B: The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.
Explanation
To better understand this statement, we need to understand the concept of present value and its relationship with interest rates and time periods.
Present value is the current value of a future sum of money, discounted at a given interest rate. In other words, it is the amount of money that we need to invest today to receive a certain amount of money in the future, based on the expected rate of return.
Now, let's consider the following scenarios:
- The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.
This statement is true because the longer the time period, the more time the money has to grow and accumulate interest. Therefore, the present value will be smaller because we need to invest less money today to achieve the same future value.
- A future dollar is always less valuable than a dollar today if interest rates are positive.
This statement is also true because of the time value of money. Money today is worth more than the same amount of money in the future because we can invest it and earn interest.
- The discount factor is the reciprocal of the compound factor.
This statement is true because the discount factor is used to calculate the present value of a future sum of money, while the compound factor is used to calculate the future value of a present sum of money. The two factors are inversely related, meaning that the discount factor is the reciprocal of the compound factor.
- The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.
This statement is false because the higher the interest rate, the more valuable money is in the future. Therefore, the present value will be smaller because we need to invest less money today to achieve the same future value.
Conclusion
In summary, the false statement is option B. The greater the interest rate, the smaller the present value, given a $100 future value and holding the time period constant.
Option B: The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.
Explanation
To better understand this statement, we need to understand the concept of present value and its relationship with interest rates and time periods.
Present value is the current value of a future sum of money, discounted at a given interest rate. In other words, it is the amount of money that we need to invest today to receive a certain amount of money in the future, based on the expected rate of return.
Now, let's consider the following scenarios:
- The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.
This statement is true because the longer the time period, the more time the money has to grow and accumulate interest. Therefore, the present value will be smaller because we need to invest less money today to achieve the same future value.
- A future dollar is always less valuable than a dollar today if interest rates are positive.
This statement is also true because of the time value of money. Money today is worth more than the same amount of money in the future because we can invest it and earn interest.
- The discount factor is the reciprocal of the compound factor.
This statement is true because the discount factor is used to calculate the present value of a future sum of money, while the compound factor is used to calculate the future value of a present sum of money. The two factors are inversely related, meaning that the discount factor is the reciprocal of the compound factor.
- The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.
This statement is false because the higher the interest rate, the more valuable money is in the future. Therefore, the present value will be smaller because we need to invest less money today to achieve the same future value.
Conclusion
In summary, the false statement is option B. The greater the interest rate, the smaller the present value, given a $100 future value and holding the time period constant.
Free Test
FREE
| Start Free Test |
Community Answer
Which of the following is false?a)The longer the time period, the smal...
Answer:B
Explanation:
Rather than explaining theoretically,I can explain this mathematically to make you understand better
If we go with option A,then it is given that present value decreases with an increase in time period when the future value and the interest rate are constant.
With the given formula of present value of annuity,we can observe that the present value is the numerator in the LHS of the formula whereas the time period is the denominator in the same side.As we know that a numerator and denominator has adverse affects in each other,thus here it is obvious that the time period and present value of annuity are in a negative relationship.Thus held that this statement is true AND NOT FALSE
If we go with option D,it says that the discount factor is the reciprocal of the compound factor.We know that compounding is the method of finding future value of present investment whereas discounting is the method of finding the present value of future cash flows.Thus they both are reciprocal terms
We can mathematically show discounting as PV=FV/(1+r)^n and compounding as FV=PV(1+r)^n.Therefore it is also mathematically show that these are reciprocal terms.So this statement is true AND NOT FALSE
If we go with option C,it is given that the future value of a dollar is always less than the present value when interest rates are postive.If we take the formula of present value of annuity,the interest rate and time period are in denominator and thus they both always tends to decrease the value of money but never increase and so this statement holds good.Thus this is also true AND NOT FALSE
If we go with option B,it is given that the interest rates and present value are in postive relationship if other things(time period,future value of annuity) remains constant.If we take the formula of present value of annuity,present value is in the numerator and interest rates are in the favour of denominator.So they both are likely to have a negative relationship(ceterus parabus) but it is given as a positive relationship.Thus,THIS STATEMENT IS FALSE
Explanation:
Rather than explaining theoretically,I can explain this mathematically to make you understand better
If we go with option A,then it is given that present value decreases with an increase in time period when the future value and the interest rate are constant.
With the given formula of present value of annuity,we can observe that the present value is the numerator in the LHS of the formula whereas the time period is the denominator in the same side.As we know that a numerator and denominator has adverse affects in each other,thus here it is obvious that the time period and present value of annuity are in a negative relationship.Thus held that this statement is true AND NOT FALSE
If we go with option D,it says that the discount factor is the reciprocal of the compound factor.We know that compounding is the method of finding future value of present investment whereas discounting is the method of finding the present value of future cash flows.Thus they both are reciprocal terms
We can mathematically show discounting as PV=FV/(1+r)^n and compounding as FV=PV(1+r)^n.Therefore it is also mathematically show that these are reciprocal terms.So this statement is true AND NOT FALSE
If we go with option C,it is given that the future value of a dollar is always less than the present value when interest rates are postive.If we take the formula of present value of annuity,the interest rate and time period are in denominator and thus they both always tends to decrease the value of money but never increase and so this statement holds good.Thus this is also true AND NOT FALSE
If we go with option B,it is given that the interest rates and present value are in postive relationship if other things(time period,future value of annuity) remains constant.If we take the formula of present value of annuity,present value is in the numerator and interest rates are in the favour of denominator.So they both are likely to have a negative relationship(ceterus parabus) but it is given as a positive relationship.Thus,THIS STATEMENT IS FALSE
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer?
Question Description
Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer?.
Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following is false?a)The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant.b)The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant.c)A future dollar is always less valuable than a dollar today if interest rates are positive.d)The discount factor is the reciprocal of the compound factor.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup