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John deposited $10,000 to open a new savings account that [#permalink]
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16 Jul 2012, 04:36
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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
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Re: John deposited $10,000 to open a new savings account that [#permalink]
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16 Jul 2012, 11:16
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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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Re: John deposited $10,000 to open a new savings account that [#permalink]
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16 Jul 2012, 12:54
D.
SI = (P*R*T) / 100 SI after 1st Quarter: (10,000*4*3/12) /100 = 100 Principal for 2nd Quarter = 10,000+ 101 = 10100 SI after 2nd Quarter: (10,101*4*3/12) /100 = 101 Amount after 2nd Quarter (6 months) = 10100 +101 = 10,201



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Re: John deposited $10,000 to open a new savings account that [#permalink]
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20 Jul 2012, 03:03
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SOLUTIONJohn 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. Answer: D. Hope it's clear.
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Re: John deposited $10,000 to open a new savings account that [#permalink]
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14 Aug 2013, 02:38



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Re: John deposited $10,000 to open a new savings account that [#permalink]
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18 Oct 2013, 12:46



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Re: John deposited $10,000 to open a new savings account that [#permalink]
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23 May 2015, 06:05
10000*1,01*1,01 = 10201
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Re: John deposited $10,000 to open a new savings account that [#permalink]
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18 Jul 2015, 17:15
I am new to the forum, starting on GMAT studying. I saw the solutions, but we are not using the calculator on test day so I do not understand thanks



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Re: John deposited $10,000 to open a new savings account that [#permalink]
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18 Jul 2015, 21:16
Amount in John's A/c after 6 months = ($10,000 * 1%) + [($10,000 * 1%) * 1%] = $10,201. Ans (D).
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Re: John deposited $10,000 to open a new savings account that [#permalink]
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27 Jan 2016, 06:10
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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Re: John deposited $10,000 to open a new savings account that [#permalink]
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13 Mar 2017, 09:04
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