Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jul 1011:00 AM PDT
-11:00 AM PDT
In our conversation, Kishore talks about how strategically he used data analytics to identify high impact areas to focus on as well as his early morning study routine (3 AM prep!) that optimized his GMAT preparation.- Jun 30
08:00 AM PDT
-11:59 PM PDT
Join us June 30th for 2 weeks of GMAT questions (just 8 per day) to help with your prep and to compete with your fellow GMAT Clubbers for a chance to win a prize fund of $30,000 for you and your team-mates! - Jul 09
11:00 AM PDT
-12:30 PM PDT
Welcome to the M7 MBA Spotlight Series, featuring MIT Sloan School of Management! This video is part of GMAT Club’s exclusive MBA Spotlight event, where top business schools meet prospective applicants like you. 
Jul 0901:00 PM EDT
-02:00 PM EDT
More Target Test Prep students are earning 100th percentile GMAT scores. Don’t settle for less when the Target Test Prep course gives you everything you need to score high on the GMAT. Start your 5-day free trial today.
Jul 1206:30 AM PDT
-08:30 AM PDT
Join our webinar to master GMAT RC Main Point Questions! Learn effective strategies to decipher passage themes and purposes. Senior Verbal Expert- Sunita Singhvi will equip you with tools to navigate complexities and avoid common traps set by the GMAT.
Jul 1211:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Jul 1311:00 AM EDT
-12:30 PM EDT
Looking for your GMAT motivation to break through the score plateau? Pragati improved her score by massive 160 points with strategic guidance and hard-work! Find out how personalized mentorship and a strong mindset can turn GMAT struggles into success.
Jul 1508:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Jul 1611:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
03 Dec 2023, 13:08
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
69% (02:25) correct
31%
(02:45)
wrong
based on 697
sessions
History
Date
Time
Result
Not Attempted Yet
Hans invested 10,000 at an annual interest rate of x percent, compounded annually. If the annual interest rate of x percent had been compounded semiannually, how much more interest, in dollars, would he have earned of his 10,000 investment for the first year in terms of x?
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
03 Dec 2023, 13:45
Kudos
Bookmarks
XimeSol
Hans invested 10,000 at an annual interest rate of x percent, compounded annually. If the annual interest rate of x percent had been compounded semiannually, how much more interest, in dollars, would he have earned of his 10,000 investment for the first year in terms of x?
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
In a year, $10,000 at an annual interest rate of x percent, compounded annually, earns an interest of \(10,000*\frac{x}{100} = 100x\).
When x percent is compounded semiannually, it implies applying x/2 percent twice a year. So, $10,000 would earn:
- \(10,000*(1 + \frac{(\frac{x}{2})}{100})^2 - 10,000 = \)
\(= 10,000*(1 +\frac{ x}{200})^2 - 10,000 = \)
\(= 10,000*(1 + \frac{x}{100} + \frac{x^2}{40,000}) - 10,000 = \)
\(= 10,000 + 100x + \frac{x^2}{4} - 10,000 = \)
\(= 100x + \frac{x^2}{4}\).
Therefore, the difference would be:
- \(100x + \frac{x^2}{4} - 100x = \frac{x^2}{4}\).
Answer: E.
03 Dec 2023, 13:40
Kudos
Bookmarks
XimeSol
Hans invested 10,000 at an annual interest rate of x percent, compounded annually. If the annual interest rate of x percent had been compounded semiannually, how much more interest, in dollars, would he have earned of his 10,000 investment for the first year in terms of x?
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
(A) \(50x\)
(B) \(100x\)
(C) \(100x + \frac{x^2}{4}\)
(D) \(\frac{x^2}{2}\)
(E) \(\frac{x^2}{4}\)
One way is to solve this algebraic, and another way is to assume values to solve this question.
Let x = 4%
...Hans invested 10,000 at an annual interest rate of x percent, compounded annually...
Interest Earned = \(10000 * \frac{4}{100 }= 400\)
...If the annual interest rate of x percent had been compounded semiannually...
Amount = \(10000 * (1+\frac{4}{200})^2 = 10000 * (\frac{51}{50})^2\)
= \((51)^2 * 4 = (50+1)^2*4 = 10404\)
Interest Earned = $\(404\)
...how much more interest, in dollars, would he have earned of his 10,000 investment for the first year....
Difference in Interest Earned = \(404 - 400 = 4\)
Answer Choice Elimination
(A) \(50x\) ⇒ \(50 * 4 \neq 4\)⇒ Eliminate
(B) \(100x\) ⇒ \(100 * 4 \neq 4\)⇒ Eliminate
(C) \(100x + \frac{x^2}{4}\) ⇒ \(100x + \frac{4^2}{4} \neq 4\)⇒ Eliminate
(D) \(\frac{x^2}{2}\) ⇒ \(\frac{4^2}{2} \neq 4\)⇒ Eliminate
(E) \(\frac{x^2}{4}\) ⇒ \(\frac{4^2}{4} = 4\)⇒ Answer
Option E
