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John deposited $10,000 to open a new savings account that [#permalink] Show Tags 16 Jul 2012, 03:36 2 This post received KUDOS Expert's post 12 This post was BOOKMARKED 00:00 Difficulty: 25% (medium) Question Stats: 71% (01:59) correct 29% (01:17) wrong based on 845 sessions HideShow timer Statistics 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 (8)$10,101
(e) $10,200 (D)$10,201
(E) $10,400 Diagnostic Test Question: 21 Page: 23 Difficulty: 650 [Reveal] Spoiler: OA _________________ Intern Joined: 11 Jul 2011 Posts: 19 Location: India Concentration: Entrepreneurship, Marketing GMAT Date: 03-08-2013 WE: Manufacturing and Production (Manufacturing) Followers: 0 Kudos [?]: 9 [1] , given: 6 Re: John deposited$10,000 to open a new savings account that [#permalink]

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16 Jul 2012, 10:16
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john amount is compounded quarterly so the formula is A=P*(1+R/100)^N her p=principle R=rate of interest N=no of terms
rate of interest is 4% for a yr
so for quarter R=4/4=1%
john receive amt after 6 mnts so there are two quarter
so N=2
Amount A=P(1+R/100)^2
=10000(1+1/100)^2
=10000(1+0.01)^2
=10201
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20 Jul 2012, 02:03
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SOLUTION

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
(8) $10,101 (e)$10,200
(D) $10,201 (E)$10,400

Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 moths.

For the first 3 moths interest was 1% of $10,000, so$100;
For the next 3 moths interest was 1% of $10,000, plus 1% earned on previous interest of$100, so $100+$1=$101; Total interest for 6 months was$100+$101=$201, hence balance after 6 months was $10,000+$201=$10,201. Answer: D. Approach #2: If the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of$10,000, so $200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than$200, only answer choice D fits.

Hope it's clear.
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18 Oct 2013, 11:46
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23 May 2015, 05:05
10000*1,01*1,01 = 10201
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18 Jul 2015, 20:16
Amount in John's A/c after 6 months = ($10,000 * 1%) + [($10,000 * 1%) * 1%] = $10,201. Ans (D). _________________ I used to think the brain was the most important organ. Then I thought, look what’s telling me that. Intern Joined: 18 Jan 2016 Posts: 25 Followers: 0 Kudos [?]: 2 [0], given: 7 Re: John deposited$10,000 to open a new savings account that [#permalink]

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27 Jan 2016, 05:10
Bunuel wrote:
Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 months.

Although this is the method they are looking for, the question is poorly worded. By explicitly saying that 4% was earned, this implies that 4% was the effective rate, and not nominal.
Would have been better to say "the account earned a nominal annual interest rate of 4%". No more confusion.
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