Jane's investment of $200 increased by 200% in 7 years when compounded

Question

Jane's investment of $200 increased by 200% in 7 years when compounded annually. If she wants to earn an additional compound interest of $4800, for how many more years should she keep her money invested?

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

stonecold · Accepted Answer

Nice one.
Here is what i did ==>

In 7 years => 200 becomes => 600

So the value becomes thrice of itself in every 7 years.

200-------600------1800------5400------

After 7 years->For an additional $4800 => Value must be 600+4800=> $5400

Hence she must wait an additional 14 years.

Smash that B.

NikGujju · Answer

in every 7 years, the value rises by 200%. Now, with the investment of 200, if one needs to have 200% profits, the value will be 600.
 The gain of 4800 above this would be 600. In another 7 years, 600 will be 1800 with gain of 1200 and in another 7 years, it shall be 5400 with gain of 4800.
 Boom!!

Always remember, GMAT do not want to test your understanding on math, but your analytical skills. They do not want us to remember complex formulas so a little common sense should suffice.

BTW, B is the answr.

EgmatQuantExpert · Answer

Reserving this space to post the official solution.

zanaik89 · Answer

Im not sure how u got 600 because 200 increased by 200% in 7 years when compounded annually will be much higher...

Could u pls explain?

I don't know if I have understood it right..

Thanks in advance..

ScottTargetTestPrep · Answer

We see that the original investment actually triples from $200 to $600 in 7 years . So it will triple again in another 7 years, from $600 to $1800. It will again triple in 7 more years, from $1800 to $5400. At this point, we see that the earning in additional interest is exactly 5400 - 600 = $4800. Therefore, it takes 7 + 7 = 14 additional years to earn $4800 after the investment accumulated to $600.

Answer: B

Akshaynandurkar · Answer

200$ became 600$ and we need to make additional 4800$ after 600$ which totals = 5400
now we know 200(1+r/100)^7 = 600
(1+r/100) = 3^1/7

600(1+r/100)^n = 5400
3^n/7 = 3^2
n/7 = 2 
n = 14

ZIX · Answer

Here's an algebraic solution:

600 = 200(1+i)^7 ; an increase by 200% is a 3x increase 
 3= (1+i)^7  -- (1)

Now she wants to earn 4800 additional interest. That means she wants to earn 600 + 4800 = 5400 total.

5400 = 200*(1+i)^{7+x} ; where x = additional time after 7 years. 
 5400 = 200*(1+i)^7*(1+i)^x

Substitute  3= (1+i)^7  and simplify

9 = (1+i)^x ; now if you square eq (1) on both sides you get  3^2 = (1+i)^{7*2} 
Therefore,  9 = (1+i)^{14}

And time after initial 7 years = 14 years

Kinshook · Answer

Jane's investment of $200 increased by 200% in 7 years when compounded annually.

If she wants to earn an additional compound interest of $4800, for how many more years should she keep her money invested?

Let the rate of interest be r per annum

200 + 200%*200 = 600 = 200 (1+r)ˆ7
(1+r)ˆ7 = 3

Let the number of years she should keep the money be n.
For additional compound interest of $4800
600+4800 = 600(1+r)ˆn
(1+r)ˆn = 9 = 3ˆ2 = ((1+r)ˆ7)ˆ2 = (1+r)ˆ14
n = 14

IMO B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Jane's investment of $200 increased by 200% in 7 years when compounded

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Jane's investment of $200 increased by 200% in 7 years when compounded

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards