A certain sum was invested in a high-interest bond for which

Question

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.

fluke · Accepted Answer

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.

Combining both;

r= 0.4
 2P*(1+\frac{0.4}{12})=2744

Now, we can get approx value of P.

Ans: "C"

KarishmaB · Answer

This question reminds me:

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.

punyadeep · Answer

thnx so much fluke
regards

IanStewart · Answer

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.

jko · Answer

Good point Ian, based on (2) I could easily say "initial investment is between $0 and $1372, approximately"

144144 · Answer

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.

fluke · Answer

From the stem, please see the  highlighted  part.

gurpreetsingh · Answer

Not a Gmat question. Do not waste your time.

enigma123 · Answer

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.

can someone please have a look into this and let me know how to solve this? :cry:

u0422811 · Answer

So we now there was an investment in a bond that compounds monthly for X months. X is a whole number so no fractional months, and that the value of the bond doubled in our X months of investment.

Statement 1 - gives us not info about value - granted we can back into a range of X but a dollar amount is impossible - insuff.
Statement 2- gives us a value at X+1, but its impossible to determine the starting value as we do not know either the interest rate or the starting value - insuff.

Together you have a range of rates and a X-1 ending value. Since the starting value doesn't have to be an integer and the interest rate doesn't have to be an integer either their are a number of possible answers for this.

I would say it should be E.

arjunbt · Answer

Answer is C. 
You can find a good explanation here:  https://www.urch.com/forums/gmat-math/20537-interest-rates.html

Bowtie · Answer

I decided on C after three mins, but it was more of a guess off of what I know rather than confirmation. Just hope you don't get one of these on the test

divineacclivity · Answer

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.
**********************************

Bunuel · Answer

This is a poor quality question. Check here: a-certain-sum-was-invested-in-a-high-interest-bond-for-which-110991.html#p893606

bumpbot · Answer

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A certain sum was invested in a high-interest bond for which

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