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Marcus deposited $8,000 to open a new savings account that [#permalink] Show Tags 29 Feb 2012, 17:08 1 This post received KUDOS 3 This post was BOOKMARKED 00:00 Difficulty: 15% (low) Question Stats: 76% (02:12) correct 24% (01:30) wrong based on 437 sessions HideShow timer Statistics Marcus deposited$8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?

(A) $8,200 (B)$8,205
(C) $8,400 (D)$8,405
(E) $8,500 [Reveal] Spoiler: Guys - I know a very simple question. But, I am not getting the right answer. WHy? I am using A = P(1+R/200] $$^ 2n$$ A = 8000 (1+0.05/200) ^ 2 * 6/12 = > 40(200.05) ^ 1 = 8002. So where I have got this wrong? [Reveal] Spoiler: OA _________________ Best Regards, E. MGMAT 1 --> 530 MGMAT 2--> 640 MGMAT 3 ---> 610 GMAT ==> 730 Manager Joined: 03 Feb 2012 Posts: 56 Location: United States (WI) Concentration: Other Schools: University of Wisconsin (Madison) - Class of 2014 GMAT 1: 680 Q46 V38 GMAT 2: 760 Q48 V46 GPA: 3.66 WE: Marketing (Manufacturing) Followers: 0 Kudos [?]: 27 [0], given: 12 Re: Compound Interest [#permalink] Show Tags 29 Feb 2012, 18:00 1 This post was BOOKMARKED This is a much simpler problem. I have never used exponents in calculating interest... Compounding period is half a year so R = 0.05 * 1/2 = 0.025 8000 * (1+ 0.025) = 8200 = total at 1/2 year 8200 * (1+ 0.025) = 8405 = total at year-end Shortcut = figure total at year end for annually compounding interest... 8000 * (1 + .05) = 8400. More frequent compounding results in ever-so-slightly increased totals so 8405 fits. Intern Joined: 24 Feb 2012 Posts: 33 Followers: 0 Kudos [?]: 15 [0], given: 18 Re: Compound Interest [#permalink] Show Tags 29 Feb 2012, 21:58 enigma123 wrote: A = 8000 (1+0.05/200) ^ 2 * 6/12 = > 40(200.05) ^ 1 = 8002. So where I have got this wrong? 8000 ( 1 + 5/200 )^(2*1) Math Expert Joined: 02 Sep 2009 Posts: 36590 Followers: 7092 Kudos [?]: 93378 [2] , given: 10557 Re: Compound Interest [#permalink] Show Tags 29 Feb 2012, 22:39 2 This post received KUDOS Expert's post 5 This post was BOOKMARKED Marcus deposited$8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?
(A) $8,200 (B)$8,205
(C) $8,400 (D)$8,405
(E) $8,500 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 ways to solve this problem. Approach #1: 5 percent annual interest compounded semi-annually --> 2.5% in 6 moths. For the first 6 moths interest was 2.5% of$8,000, so $200; For the next 6 moths interest was 2.5% of$8,000, plus 2.5% earned on previous interest of $200, so$200+$5=$205;

Total interest for one year was $200+$205=$405, hence balance after one year was$8,000+ $405=$8,405.

Approach #2:
If the interest were compounded annually instead of semi-annually then in one year the interest would be 5% of $8,000, so$400. Now, since the interest is compounded semi-annually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $400, only answer choice D fits. Answer: D. Hope it's clear. _________________ Math Expert Joined: 02 Sep 2009 Posts: 36590 Followers: 7092 Kudos [?]: 93378 [0], given: 10557 Re: Marcus deposited$8,000 to open a new savings account that [#permalink]

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28 May 2013, 05:31
Bumping for review and further discussion.
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30 May 2013, 00:37
rajasami4u wrote:
Bunuel wrote:
Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened? (A)$8,200
(B) $8,205 (C)$8,400
(D) $8,405 (E)$8,500

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 ways to solve this problem.

Approach #1:
5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.

For the first 6 moths interest was 2.5% of $8,000, so$200;
For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of$200, so $200+$5=$205; Total interest for one year was$200+$205=$405, hence balance after one year was $8,000+$405=$8,405. Answer: D. Approach #2: If the interest were compounded annually instead of semi-annually then in one year the interest would be 5% of$8,000, so $400. Now, since the interest is compounded semi-annually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than$400, only answer choice D fits.

Hope it's clear.

Bunuel,

For all CI problems if the interest is given Annually and asked Quarterly or half yearly CI , then we can just divide the Percent according our need. Tats all?

Yes: 5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.
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16 Dec 2015, 06:26
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