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If P dollars borrowed or invested for t years
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14 Apr 2021, 11:31
14 Apr 2021, 11:31
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If P dollars borrowed or invested for \(t\) years at the interest rate \(r\) compounded \(n\) times per year, then the future value (a) will be \(A=P(1+\frac{r}{n})^{nt}\)
Two individuals, M and N invested P dollars with the following conditions and both gained the same future value at the end of the investment period:
M invested $P at the interest rate \(\frac{r-5}{100}\) for 6 years compounded 4 times per year
N invested $P at the interest rate \(\frac{r+5}{100}\) for 4 years compounded 6 times per year
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Two individuals, M and N invested P dollars with the following conditions and both gained the same future value at the end of the investment period:
M invested $P at the interest rate \(\frac{r-5}{100}\) for 6 years compounded 4 times per year
N invested $P at the interest rate \(\frac{r+5}{100}\) for 4 years compounded 6 times per year
Quantity A |
Quantity B |
\(r\) |
\(25\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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If P dollars borrowed or invested for t years
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14 Apr 2021, 21:42
14 Apr 2021, 21:42
1
Carcass wrote:
If P dollars borrowed or invested for \(t\) years at the interest rate \(r\) compounded \(n\) times per year, then the future value (a) will be \(A=P(1+\frac{r}{n})^{nt}\)
Two individuals, M and N invested P dollars with the following conditions and both gained the same future value at the end of the investment period:
M invested $P at the interest rate \(\frac{r-5}{100}\) for 6 years compounded 4 times per year
N invested $P at the interest rate \(\frac{r+5}{100}\) for 4 years compounded 6 times per year
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Two individuals, M and N invested P dollars with the following conditions and both gained the same future value at the end of the investment period:
M invested $P at the interest rate \(\frac{r-5}{100}\) for 6 years compounded 4 times per year
N invested $P at the interest rate \(\frac{r+5}{100}\) for 4 years compounded 6 times per year
Quantity A |
Quantity B |
\(r\) |
\(25\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
\(A_M = P [1 + \frac{(r-5)}{(100)(4)}]^{(4)(6)}\)
\(A_N = P [1 + \frac{(r+5)}{(100)(6)}]^{(6)(4)}\)
As per the question, \(A_M = A_N\)
i.e. \(P [1 + \frac{(r-5)}{(100)(4)}]^{(4)(6)} = P [1 + \frac{(r+5)}{(100)(6)}]^{(6)(4)}\)
\([1 + \frac{(r-5)}{(100)(4)}]^{(4)(6)} = [1 + \frac{(r+5)}{(100)(6)}]^{(6)(4)}\)
Taking \(24^{th}\) root both sides;
\([1 + \frac{(r-5)}{(100)(4)}] = [1 + \frac{(r+5)}{(100)(6)}]\)
\(\frac{(r-5)}{(100)(4)} = \frac{(r+5)}{(100)(6)}\)
\(\frac{(r-5)}{4} = \frac{(r+5)}{6}\)
\(6r - 30 = 4r + 20\)
\(2r = 50\)
\(r = 25\)
Col. A: \(25\)
Col. B: \(25\)
Hence, option C
Re: If P dollars borrowed or invested for t years
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22 Jul 2024, 22:34
22 Jul 2024, 22:34
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