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 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.
Jun 3008:00 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 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 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.
25 Nov 2022, 07:51
Kudos
Bookmarks
A2D2
ScottTargetTestPrep
kajolnb
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)
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
Why are multiplying with 1.08 and not 0.08
Isn’t 8% is 0.08
08 Feb 2023, 04:34
Kudos
Bookmarks
A2D2
Why are multiplying with 1.08 and not 0.08
Isn’t 8% is 0.08
Hi A2D2,
Thanks for your query.
Please observe that though the interest rate is 8%, which definitely equals 0.08, the question does not just ask for the INTEREST earned on ‘x’. Observe that the question is about the relationship between x and w, where w is the AMOUNT of the investment after 2 years. And Amount is composed of two parts: Principal + Interest.
So, we need to find the amount at the end of year 1 (to find the principal for year 2) and then, the amount at the end of year 2.
Read on to find exactly how 1.08 is the right factor to multiply here, and not just 0.08.
DETAILED EXPLANATION:
Alex initially deposited ‘x’ dollars at an 8% interest rate, compounded annually.
So, Interest earned during the first year = 8% of x = 0.08x
Hence, the amount in Alex’s account after one year
- = Initial investment + Interest earned
- = x + 0.08x = x * (1 + 0.08) = 1.08x …(I) [Observe how we got 1.08 here when we added the initial investment to the interest earned. You had stopped at the interest alone. 😊]
Now, at the beginning of the second year, Alex again deposited additional x dollars in the same account. So, the total principal at the beginning of 2nd year = final amount of the end of first year + New investment.
- Using (I), we can say, Principal at the beginning of 2nd year = 1.08x + x …(II)
Now, the final question: Amount in Alex’s account at the end of 2nd year.
Since the account still adds an annual interest of 8%, and the principal at the beginning of the second year now becomes (1.08x + x), Alex will get an interest of 8% on this new principal.
- So, INTEREST earned during second year = (1.08x + x) × 0.08
- And the FINAL AMOUNT (that is, w) after the second year = Principal + Interest
- That is, w = (1.08x + x) + [(1.08x + x) × 0.08]
- w = (1.08x + x) (1 + 0.08) [Taking (1.08x + x) common from both terms]
- = 1.08 * (1.08x + x)
Observe carefully how for both years, the interest of 0.08 becomes 1.08 because of adding the principal amount. This is exactly what confused you!
Hope this will clarify!
Best,
Aditi Gupta
Quant expert, e-GMAT
22 Jan 2025, 09:22
Kudos
Bookmarks
say x = 1
At the end of 1 year it is 1.08, then 1 was deposited again. So total at the start of year 2 is 2.08. At the end you have 2.08 and the interest earned on this amount.
So the total at the end, i.e. w = 2.08 * 1.08
\(\frac{w}{(2.08 * 1.08) }= 1\)
Get it to a form to match the answer choices
\(\frac{w}{(1.08 + 1.08^2) }= x\) (as x = 1)
At the end of 1 year it is 1.08, then 1 was deposited again. So total at the start of year 2 is 2.08. At the end you have 2.08 and the interest earned on this amount.
So the total at the end, i.e. w = 2.08 * 1.08
\(\frac{w}{(2.08 * 1.08) }= 1\)
Get it to a form to match the answer choices
\(\frac{w}{(1.08 + 1.08^2) }= x\) (as x = 1)
kajolnb
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. \(\frac{w}{1+1.08}\)
B. \(\frac{w}{1.08+1.16}\)
C. \(\frac{w}{1.16+1.24}\)
D. \(\frac{w}{1.08+1.08^2}\)
E. \(\frac{w}{1.08^2+1.08^2}\)
A. \(\frac{w}{1+1.08}\)
B. \(\frac{w}{1.08+1.16}\)
C. \(\frac{w}{1.16+1.24}\)
D. \(\frac{w}{1.08+1.08^2}\)
E. \(\frac{w}{1.08^2+1.08^2}\)
