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A certain sum was invested in a high-interest bond for which [#permalink]
16 Mar 2011, 06:49

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E

Difficulty:

(N/A)

Question Stats:

38% (02:21) correct
62% (01:02) wrong based on 11 sessions

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.

Re: compound intrest [#permalink]
16 Mar 2011, 07:40

1

This post received KUDOS

punyadeep wrote:

Q 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.

Investment = $P time: x months = x/12 years Periods = n = 12

Return after application of the compound Interest for x months;

P(1+\frac{r}{n})^{nt} P(1+\frac{r}{12})^{12*x/12} P(1+\frac{r}{12})^x It is given that the investment doubles after x months; P(1+\frac{r}{12})^x=2P (1+\frac{r}{12})^x=2

r and x are unknown

1. 0.4<=r<=0.44 (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P. Not Sufficient.

2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient.

Re: compound intrest [#permalink]
16 Mar 2011, 21:19

Where is this question from? It makes no sense, in DS, to ask for the 'approximate value' of something -- how could you possibly know what information would be sufficient? If I ask the following question:

What is the approximate value of x?

1. 3 < x < 5 2. 4 < x < 4.5

Is Statement 1 sufficient? Statement 2? You can't possibly know. It's a nonsensical question to ask in DS, so I wouldn't use other questions from the same source. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: compound intrest [#permalink]
18 Mar 2011, 09:37

Fluke - how did u go from the 2nd stage to the 3rd?!?!

2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. _________________

Re: compound intrest [#permalink]
18 Mar 2011, 10:00

144144 wrote:

Fluke - how did u go from the 2nd stage to the 3rd?!?!

2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient.

From the stem, please see the [highlight]highlighted[/highlight] part.

fluke wrote:

Investment = $P time: x months = x/12 years Periods = n = 12

Return after application of the compound Interest for x months;

P(1+\frac{r}{n})^{nt} P(1+\frac{r}{12})^{12*x/12} P(1+\frac{r}{12})^x It is given that the investment doubles after x months; P(1+\frac{r}{12})^x=2P [highlight]--------------A[/highlight] (1+\frac{r}{12})^x=2

r and x are unknown

1. 0.4<=r<=0.44 (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P. Not Sufficient.

2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 [highlight]Substitute from equation A[/highlight] 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient.

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.

Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you. ********************************** (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P. **********************************

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.

Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you. ********************************** (1+\frac{0.4}{12})^x=(1.033)^x = 2 to (1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P. **********************************

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