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On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 01:04
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80% (00:54) correct 20% (01:49) wrong based on 44 sessions
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Competition Mode Question On January, 1, 2002, Michael invested a certain amount of money at r percent interest rate, compounded annually. What is the value of r? (1) At the end of 2004, the investment plus the total interest was $ 5,955. (2) At the end of 2006, the investment plus the total interest was $ 6,690.
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 01:44
IMO answer is option C Posted from my mobile device
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 01:58
We have two unknown variables, that is r and amount invested, A. We know r is annual compound interest rate of the investment.
Statement 1 is not sufficient because we are able to generate the following equation from it. 5,955=A(1+r)^2......(1) Since we don't know A the investment amount, we cannot determine r.
2. Similar to statement 1 above, we can derive the following equation 6,690=A(1+r)^4...... (2) Since we don't know A, the investment amount, we are unable to determine r.
1+2 is however sufficient. We have two equations and two variables so we can substitute for A and find r or divide (2) by (1) and solve for r.
The answer is therefore C.



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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 02:33
Find r (interest rate)
1. At the end of 2004, total interest = 5955 Start investing from beginning of 2002  n=3
(r+1)^3 = 5955 Can solve for r  sufficient
2. At the end of 2006, total interest =6690 N=5
(r+1)^5 = 6690 Can solve for r  sufficient
Therefore, D is the correct answer.
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 02:43
On January, 1, 2002, Michael invested a certain amount of money at r percent interest rate, compounded annually. What is the value of r?
(1) At the end of 2004, the investment plus the total interest was $ 5,955. (2) At the end of 2006, the investment plus the total interest was $ 6,690.
let principal amount =x so interest = p*r*t/100 #1At the end of 2004, the investment plus the total interest was $ 5,955. 5955= interest at 2004 end "a" principal ; 5955=x+a ; a = 5955x 5955x=x*r*2/100 value of x & r is unkown insufficient #2 At the end of 2006, the investment plus the total interest was $ 6,690. 6690x=x*r*4/100 again in sufficient from 1 &2 we can solve linearly value of r IMO C



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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 08:09
Since the amount is compounded annually; final amount will be calculated using the formula =>
P(1 + r/100)^n
where P is invested Principle amount, r is rate of interest and n is no of years after which amount is being calculated
Statement 1: Final Amount = 5955 = P(1+r/100)^2 => only 1 equation and 2 unknown variables (P and R)
Statement 2: Final Amount = 6690 = P(1+r/100)^4 => only 1 equation and 2 unknown variables (P and R)
Combining both statements: Eq in Statement 2/ Eq in Statement 1 => 6690/5955 = (1 + r/100)^2 : thus r can be calculated.
So Ans: C



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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 11:01
Let Principle amount on January, 1, 2002 = P. Number of years = n Interest rate = r = ? (1) At the end of 2004, the investment plus the total interest was $ 5,955. At the end of 2004, there are total 3 years i.e. n = 3. Now, \(A2004 = P(1+\frac{r}{100})^3\) \(5955 = P(1+\frac{r}{100})^3\) Two variable which can take any value. INSUFFICIENT. (2) At the end of 2006, the investment plus the total interest was $ 6,690. At the end of 2006, there are total 5 years i.e. n = 5. Now, \(A2006 = P(1+\frac{r}{100})^5\) \(6690 = P(1+\frac{r}{100})^5\) Two variable which can take any value. INSUFFICIENT. Together 1) and 2) \(A2006  A2004 = P(1+\frac{r}{100})^5  P(1+\frac{r}{100})^3\) \(6690 – 5955 = P(1+\frac{r}{100})^5  P(1+\frac{r}{100})^3\) \(735 = P(1+\frac{r}{100})^5  P(1+\frac{r}{100})^3\) Again two variable which can take any value. INSUFFICIENT. Answer (E).
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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06 Sep 2019, 21:08
IMO it's C. Because from each of the statements we cannot get the value of Principal and Rate as two variables are there but on combining we can get the value of R and then we can get P.
On January, 1, 2002, Michael invested a certain amount of money at r percent interest rate, compounded annually. What is the value of r? (1) At the end of 2004, the investment plus the total interest was $ 5,955. (2) At the end of 2006, the investment plus the total interest was $ 6,690.
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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08 Sep 2019, 04:39
Given; On January, 1, 2002, Michael invested a certain amount of money at r percent interest rate, compounded annually. Asked: What is the value of r? Let \(A = P (1+r)^n\) (1) At the end of 2004, the investment plus the total interest was $ 5,955. \(5955 = P (1+r)^2\) Since P & r are unknown NOT SUFFICIENT (2) At the end of 2006, the investment plus the total interest was $ 6,690. \(6690 = P(1+r)^4\) Since P & r are unknown NOT SUFFICIENT Combining (1) & (2) (1) At the end of 2004, the investment plus the total interest was $ 5,955. \(5955 = P (1+r)^2\) (2) At the end of 2006, the investment plus the total interest was $ 6,690. \(6690 = P(1+r)^4\) Since there 2 equations and 2 unknowns We can get values of P & r Divide equation 2 by equation 1, we get 6690/5955 = (1+r)^2 r = 6% approximately IMO C
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Re: On January, 1, 2002, Michael invested a certain amount of money at r p
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