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Stormgal

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A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars?

 

1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent.

 

2) If the period of investment had been one month longer, the final sale value of the bond would have been approximately $2,744.

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I think C.

 

 

Let's say original investment amount was Y The interest rate is z% (assuming a monthly Interest rate) and x the number of months.

 

So the equation to solve this problem is

 

Y*(1+z%)^x=2Y

 

So Statement 1 gives us an approximate value for z%, but to answer the question, we really need x, the number of months.-Insuff

 

Statement 2 says Y*(1+z%)^(x+1)=2,744 or 2Y* (1+z%)=2,744

 

So this time we can find out that 2Y=2,744/(1+z%)

 

and therefore Y=2,744/[2*(1+z%)] This is Insufficient alone, but combined with an approximate value of z%, you can find an approximate value of Y, the original investment

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Source Manhattan GMAT:

 

In order to answer this question, we need to recall the compound interest formula: http://www.manhattangmat.com/images/Challenge/February72005/ee1.gif, where FV is the future value of the investment, PV is the present value, r is the interest rate, and n is the number of compounding time periods.

 

In this case, we do not know the value of any of the unknowns and are asked to find PV. We do, however, know that the value of PV doubled. Therefore, FV = 2PV. We can use this to construct and simplify the following equation:

 

http://www.manhattangmat.com/images/Challenge/February72005/ee2.gif

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continued:

 

Therefore, the interest rate http://www.manhattangmat.com/images/Challenge/February72005/ee3.gif. Now we can look at the statements.

 

Statement (1) tells us that the interest rate was between 39% and 45%. Therefore, the value of http://www.manhattangmat.com/images/Challenge/February72005/ee4.gif is between 39 and 45.

 

If n = 1, then http://www.manhattangmat.com/images/Challenge/February72005/ee5.gif. This value is not between 39 and 45. Therefore, n does not equal 1.

If n = 2, then http://www.manhattangmat.com/images/Challenge/February72005/ee6.gif. (Note that the square root of 2 is approximately 1.4.) 40 is between 39 and 45, so 2 is a possible value of n.

 

Can n be greater than 2? Since the value of r (40) is almost at the lower limit of the given range (39 to 45) when n = 2, it is not possible that increasing the value of n to 3 (resulting in our taking the cube root of 2, which is approximately 1.26) would yield a value of r that is above 39.

 

So n must equal 2 and r must be approximately 40. But this does not tell us the value of PV.

 

Statement (2) tells us that the sale value of the bond would have been approximately 2,744 if the period of investment had been one month longer. We can set up the following equation:

 

http://www.manhattangmat.com/images/Challenge/February72005/ee8.gif

 

This does not allow us to find a value for PV. Statement (2) is insufficient.

 

If we take the statements together, we can substitute the values of r and n derived from statement (1):

 

http://www.manhattangmat.com/images/Challenge/February72005/ee9.gif

 

Therefore, the approximate value of the original investment is $1,000.

 

The correct answer is C, both statements together are sufficient, but neither statement alone is sufficient.

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I just guessed C from logic..

 

there are 4 variables, rate, time, original amount, final amount

 

so if you know 3 of them u are left with 1 variable with 1 equation.

so its solvable.

 

if u have 2 unkowns u need 2 eq. , 3 unknowns 3 eq, etc etc (becareful though, sometimes the test question may trick you)

 

*edit to add comment:--

They can trick you by having 2 equations 2 unknown, but 1 of the unknown might be cancelled out and disappear so u only need 1 equation to solve it since there's only 1 unknown left.. (confusing?)

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