• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Alex deposited x dollars into a new account ##### This topic has 3 expert replies and 0 member replies ## Alex deposited x dollars into a new account Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? A. w/(1+1.08) B. w/(1.08+1.16) C. w/(1.16+1.24) D. w/(1.08+1.08^2) E. w/(1.08^2+1.08^2) D ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15380 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 rsarashi wrote: Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? A. w/(1+1.08) B. w/(1.08+1.16) C. w/(1.16+1.24) D. w/(1.08+1.08^2) E. w/(1.08^2+1.08^2) Since 8% interest is earned each year, the amount in the account after the first year = 1.08x. After Alex deposits an additional x dollars, the amount in the account = 1.08x + x. After an additional 8% is earned in the second year, the amount in the account = w = 1.08[1.08x + x)] = (1.08)Â²x + 1.08x Since w = (1.08)Â²x + 1.08x, we get: w = x(1.08Â² + 1.08) x = w/(1.08Â² + 1.08). The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE 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. Student Review #1 Student Review #2 Student Review #3 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 rsarashi wrote: Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? A. w/(1+1.08) B. w/(1.08+1.16) C. w/(1.16+1.24) D. w/(1.08+1.08^2) E. w/(1.08^2+1.08^2) We start by determining the new value of the x dollars Alex deposited into his account that earned 8 percent annual interest. At the end of the first year the amount of money in the account was 1.08x and then he added another x dollars to the account, so the account then had a total value of 1.08x + x dollars. The 1.08x + x dollars earned another 8 percent interest for the year. Thus, the total value of his account at the end of the second year is: 1.08(1.08x + x) = (1.08^2)x + 1.08x Since the new total value is equal to w, we can set up the following equation: w = (1.08^2)x + 1.08x Now we must get x in terms of w. w = x(1.08^2 + 1.08) w/(1.08^2 + 1.08) = x Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ? A. w/(1+1.08) B. w/(1.08+1.16) C. w/(1.16+1.24) D. w/(1.08+1.08^2) E. w/(1.08^2+1.08^2) Hi rsarashi, Let's take a look at your question. Amount Alex deposited in account = x dollars Annual interest earned after one year = (8%) x = 0.08x Total amount in account after one year = (x + 0.08x) = 1.08x After one year, Alex deposited additional x dollars. Total amount after depositing x dollars = 1.08x + x interest after second year = (8%)(1.08x + x) = (0.08)(1.08x + x) Total amount after second year : $$=\left(1.08x+x\right)+0.08\left(1.08x+x\right)$$ $$=\left(1.08x+x\right)\left(1+0.08\right)$$ $$=\left(1.08x+x\right)\left(1.08\right)$$ $$=\left(1.08\right)^2x+1.08x$$ $$=x\left[\left(1.08\right)^2+1.08\right]$$ Let w be the total amount in the account, then $$w=x\left[\left(1.08\right)^2+1.08\right]$$ $$x=\frac{w}{1.08^2+1.08}$$ Therefore, Option D is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 40 first replies
2 Ian Stewart 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 25 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

58 posts
4 Ian Stewart

GMATiX Teacher

49 posts
5 GMATGuruNY

The Princeton Review Teacher

38 posts
See More Top Beat The GMAT Experts