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15 Sep 2009, 14:11
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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
B) $10,101 C)$10,200
D) $10,201 E)$10,400

Official Guide 12 Question

 Question: 21 Page: 23 Difficulty: 600

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Video Explanations:

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
[Reveal] Spoiler: OA
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15 Sep 2009, 14:20
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MuffE wrote:
Pg 12 #21

John deposited $10,000 to open a new savings account that earned 4% 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

From this I got $10K*.04*6/12=$200 which means the account should have $10,200...but the answer keys says$10,201.

Is this an error or did I miss something?

This is not an error in the answer. According to the question, interest is compounded quarterly.

So annual interest = 10000*0.04 = 400
Interest acrued in a quarter = 400/4 = 100.

so the amount acrued after 6 months = (10000 + 10000*0.04/4) + (10100 + 10100*0.04/4) = 10201
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04 Feb 2012, 06:11
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MuffE 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

Official Guide 12 Question

 Question: 21 Page: 23 Difficulty: 600

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Video Explanations:

There is indeed a formula to calculate final balance for compounded interest (check here: math-number-theory-percents-91708.html) though there are at least two shorter way to solve this problem.

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, 12:46
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