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29 Feb 2012, 18:08
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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

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Re: Compound Interest [#permalink]

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29 Feb 2012, 19:00
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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.
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Re: Compound Interest [#permalink]

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29 Feb 2012, 22:58
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)
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Re: Compound Interest [#permalink]

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29 Feb 2012, 23:39
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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.

Answer: D.

Hope it's clear.
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Re: Marcus deposited $8,000 to open a new savings account that [#permalink] ### Show Tags 28 May 2013, 06:31 Expert's post Bumping for review and further discussion. _________________ Math Expert Joined: 02 Sep 2009 Posts: 33503 Followers: 5930 Kudos [?]: 73469 [0], given: 9902 Re: Compound Interest [#permalink] ### Show Tags 30 May 2013, 01:37 Expert's post 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. Answer: D. 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. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 10184 Followers: 481 Kudos [?]: 124 [0], given: 0 Re: Marcus deposited$8,000 to open a new savings account that [#permalink]

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20 Jul 2014, 21:19
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Re: Marcus deposited $8,000 to open a new savings account that [#permalink] ### Show Tags 16 Dec 2015, 07:26 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Marcus deposited$8,000 to open a new savings account that   [#permalink] 16 Dec 2015, 07:26
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# Marcus deposited \$8,000 to open a new savings account that

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