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AbeNeedsAnswers Master | Next Rank: 500 Posts
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OG John deposited $10,000 Tue Jul 25, 2017 8:19 pm Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) John deposited$10,000 to open a new savings account that earned 4 percent annual interest,
compounded quarterly. If there were no other transactions in the account, what was the amount of
money in John’s account 6 months after the account was opened?

(A) $10,100 (B)$10,101
(C) $10,200 (D)$10,201
(E) $10,400 D Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! GMAT/MBA Expert Jay@ManhattanReview GMAT Instructor Joined 22 Aug 2016 Posted: 703 messages Followed by: 17 members Thanked: 332 times Tue Jul 25, 2017 10:27 pm AbeNeedsAnswers wrote: John deposited$10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?

(A) $10,100 (B)$10,101
(C) $10,200 (D)$10,201
(E) $10,400 D We have, 1. Rate of interest = 4% per annum 2. Componung of interest = Quarterly; it means that after every quarter, the interest would be calculated. Since we have to calculate the sum at the end of the 6 months, the interest would be computed two times. Since the given rate = 4% is annual, we must get the quarterly rate, which is 4/4 = 1% per quarter * Sum at the end of 3 months = 10,000 + 10,000*1% = 10,000 + 10,000*(1/100) =$10,100
* Sum at the end of 6 months = 10,100 + 10,100*1% = 10,100 + 10,100*(1/100) = $10,201 The correct answer: D Hope this helps! Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Singapore | Doha | Lausanne | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10760 messages Followed by: 1212 members Thanked: 5144 times GMAT Score: 770 Wed Jul 26, 2017 6:27 am AbeNeedsAnswers wrote: John deposited$10,000 to open a new savings account that earned 4 percent annual interest,
compounded quarterly. If there were no other transactions in the account, what was the amount of
money in John’s account 6 months after the account was opened?

(A) $10,100 (B)$10,101
(C) $10,200 (D)$10,201
(E) $10,400 D When the number of "compounding" periods is only 2 or 3, we can just calculate the interest for each period. 4% annual interest, compounded quarterly, means that for each quarter year (3 months), we are adding an interest of 1% to the amount in the bank. We can practically do this in our head. Initial deposit =$10,000
Interest after 3 months = 1% of $10,000 =$100
Total after 3 months = $10,000 +$100 = $10,100 From here, the NEXT 3 months will yield an additional 1% of interest So, the interest for the next 3 months = 1% of$10,100 = $101 Total after 6 months =$10,100 + 101 = $10,201 = D Cheers, Brent _________________ Brent Hanneson – Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8703 messages Followed by: 460 members Thanked: 2729 times GMAT Score: 800 Wed Jul 26, 2017 6:40 pm Hi AbeNeedsAnswers, We're told that a$10,000 investment earns 4% annual interest, compounded QUARTERLY (which means that we calculate interest 4 times per year). We're asked for the total value of the investment after 6 MONTHS. This question requires that you understand the concept behind the Compound Interest Formula (and this concept is sometimes referred to as "interest on top of interest").

If we were using SIMPLE Interest, then we'd calculate just once (and the total interest would be 4% of $10,000 =$400). However, when using Compound Interest, you calculate interest more than once per year, and you have to adjust the 'math' a bit. Based on the number of calculations that you do each year, you then have to divide the interest rate by that number of terms.

Here, we calculate 4 times per year, so each interest calculation is 4%/4 = 1%.

First 3 months = $10,000(1.01) =$10,100
Second 3 months = $10,100(1.01) =$10,201

Since the prompt asks for the total after 6 months, we don't have to do any additional work.

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Rich

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Scott@TargetTestPrep GMAT Instructor
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Mon Aug 14, 2017 1:12 pm
John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened? (A)$10,100
(B) $10,101 (C)$10,200
(D) $10,201 (E)$10,400

D
Since the account compounds quarterly, John earns 0.4/4 = 0.1 or 1 percent interest each quarter.

After Q1, he earns 10,000 x 0.01 = 100 dollars interest, and thus he has a total of 10,000 + 100 = 10,100 dollars in the account after the first quarter or the first 3 months.

After Q2, John earns another 10,100 x 0.01 = 101 dollars interest.

So, after 6 months, the total amount of money in John’s account is 10,100 + 101 = 10,201 dollars.

Alternate Solution:

We can use the compound interest formula A = P[(1 + (r/n)]^nt, with P = 10,000, r = 0.04, n = 4, and t = 0.5. Thus, we have P = 10,000[1+(0.04/4)]^2 = 10,000(1.01)^2 = 10,201.

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