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Register now and save up to $200 Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Most awarded test prep in the world Now free for 30 days Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code ## Interest problem tagged by: Brent@GMATPrepNow This topic has 4 expert replies and 2 member replies Rastis Master | Next Rank: 500 Posts Joined 21 Sep 2011 Posted: 183 messages Followed by: 2 members Upvotes: 6 Target GMAT Score: 700 GMAT Score: 500 #### Interest problem Mon Dec 08, 2014 12:41 pm An investment a d dollars at k percent simple annual interest yields$600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3-year period? a) 2d/3 b) 3d/4 c) 4d/3 d) 3d/2 e) 8d/3 Mathsbuddy Master | Next Rank: 500 Posts Joined 08 Nov 2013 Posted: 447 messages Followed by: 1 members Upvotes: 25 Fri Dec 19, 2014 6:42 am d x k/100 x 2 = 600 So k/100 =300/d e x k/100 x 3 = 2400 e x 300/d x 3 = 2400 e x 3/d = 8 e = 8d/3 ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Mon Dec 22, 2014 12:47 pm Here's another pretty straightforward approach.$d at k% is currently giving us $300 a year. To get$800 a year, we'd need to multiply our principle by 8/3, since 300 * (8/3) = 800.

Hence we multiply d by (8/3), giving us (8/3)d, and we're done!

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Posted:
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Mon Dec 08, 2014 12:49 pm
Quote:
An investment of d dollars at k percent simple interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield$2,400 interest over a 3-year period?

A. 2d/3
B. 3d/4
C. 4d/3
D. 3d/2
E. 8d/3
The interest rate is irrelevant.
This problem is really about a PROPORTION.
$d invested over 2 years is equivalent to$600 in interest.
$x invested over 3 years must be equivalent to$2400 in interest.
Thus:
(d * 2)/600 = (x * 3)/2400
d/300 = x/800
d/3 = x/8
x = (8d)/3.

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GMATGuruNY@gmail.com
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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13910 messages
Followed by:
1808 members
13060
GMAT Score:
790
Mon Dec 08, 2014 12:49 pm
Quote:
An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield$2,400 interest over a 3-year period

2d/3
3d/4
4d/3
3d/2
8d/3
An alternate approach is to PLUG AND CHUG:
1. Choose a good value for k.
2. Use the value of k to determine the value of d.
3. Answer the question and get a target.
4. Determine which answer choice yields the target.

Step 1:
Let the interest rate = 100%:
k=100.

Step 2:
Since $600 is earned over 2 years,$300 is earned each year.
To earn $300 at an interest rate of 100%, the amount invested =$300:
d=300.

Step 3:
To earn $2400 over 3 years,$800 must be earned each year.
To earn $800 at an interest rate of 100%, the amount invested = 800. This is the target. Step 4: Now plug d=300 into the answers to see which yields the target of 800. A quick scan of the answers reveals that only E works: 8d/3 = 8(300)/3 = 800. The correct answer is E. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. Rastis Master | Next Rank: 500 Posts Joined 21 Sep 2011 Posted: 183 messages Followed by: 2 members Upvotes: 6 Target GMAT Score: 700 GMAT Score: 500 Mon Dec 08, 2014 1:00 pm That makes more sense. I was trying to use the interest rate formula and ended up guessing and moving on. Thanks! ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11283 messages Followed by: 1225 members Upvotes: 5254 GMAT Score: 770 Mon Dec 08, 2014 5:01 pm Quote: "An investment of d dollars at k percent simple annual interest yields$600 over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period? (A) 2d/3 (B) 3d/4 (C) 4d/3 (D) 3d/2 (E) 8d/3 An investment of d dollars at k percent simple annual interest yields$600 over a 2-year period.
In other words, an investment of d dollars yields $300 in interest each year. What dollar amount invested at the same rate will yield$2,400 interest over a 3-year period?
In other words, how much money must we invest to earn $800 in interest EACH YEAR? If a d dollar investment yields$300 in interest EACH YEAR, then:
- a 2d dollar investment would yield $600 (2 times$300) in interest EACH YEAR
- a 3d dollar investment would yield $900 (3 times$300) in interest EACH YEAR
- a 4d dollar investment would yield $1200 (4 times$300) in interest EACH YEAR
- etc.

From here there are two approaches.

APPROACH #1
We want the ANNUAL interest to be $800. This means we must invest an amount that is BETWEEN 2d dollars and 3d dollars [since$800 is BETWEEN $600 and$900].
When we check the answer choices, only E, which can be written as (8/3)d, is BETWEEN 2d dollars and 3d
So, the correct answer must be E

APPROACH #2
To increase the ANNUAL interest from $300 to$800, we must invest 800/300 TIMES as much money.
800/300 = 8/3, so we must invest (8/3)d dollars [aka 8d/3 dollars]

Cheers,
Brent

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