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John deposited $10,000 to open a new savings account that [#permalink]
16 Jul 2012, 03:36
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Difficulty:
25% (medium)
Question Stats:
70% (01:57) correct
30% (01:15) wrong based on 593 sessions
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?
Re: John deposited $10,000 to open a new savings account that [#permalink]
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
Re: John deposited $10,000 to open a new savings account that [#permalink]
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?
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.
Re: John deposited $10,000 to open a new savings account that [#permalink]
19 Oct 2014, 07:48
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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.
gmatclubot
Re: John deposited $10,000 to open a new savings account that
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27 Jan 2016, 05:10
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