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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.

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 Bumping for review and further discussion. _________________ Kudos [?]: 128901 [0], given: 12183 Math Expert Joined: 02 Sep 2009 Posts: 41891 Kudos [?]: 128901 [0], given: 12183 Re: Compound Interest [#permalink] ### Show Tags 30 May 2013, 01:37 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.

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. _________________ Kudos [?]: 128901 [0], given: 12183 GMAT Club Legend Joined: 09 Sep 2013 Posts: 16651 Kudos [?]: 273 [0], given: 0 Re: Marcus deposited$8,000 to open a new savings account that [#permalink]

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Re: Marcus deposited $8,000 to open a new savings account that [#permalink] ### Show Tags 21 Jun 2017, 03:19 enigma123 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 [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? The basic formula for this question is compounded interest- Payment(1 + r)^nt where r= rate of interest- that is...how much percent? n= number of times per year - this is key- this is what sets compounded interest apart from simple interest t= year- or really this variable is just equal to 1- well for the sake of this formula on the GMAT- advanced finance is different But the theory behind this formula is actually quite simple within the context of other GMAT percentage formulas...here's why. When we want to express a percentage increase such as a 20% increase of$100.00 on a stock then we would actually multiply the payment amount $100.00 by 1.2- if we wanted to express a 100% percent increase of that$100.00 we would multiply by "2" and if we wanted to express a 120 increase of $100.00 we would multiply by "2.2" - NOTE: a 150% increase is not the same as 150% of a number. The latter is warning is basically the idea of finance- you have a payment which is represented by P in the both the compounded and simple interested formula. The parentheses is quite simple if you understand the previously mentioned technique for percentage increase- the parentheses 1 + "r" or rate of interest is basically just that... we had 1 just like we did with a 20 percent increase of 1 ($100.00 x (1.2). The exponent in the formula simply expresses...well how many times are we doing that? So if you put down a $100.00 dollar stock on Tesla and it increases 20 percent every year then the amount we would have in two[u][/u] years is just$100(1.20)^2 which is really just $100(1 +20/100)^2 or in even in another form$100(1 +.20)^2

Anyways so what we have here is

$8,000.00(1 + .025)^2 ... this is the same as$8,000.00(1 + 25/100)^2 or even $8,000(1.025)^2 Thus "D" Kudos [?]: 35 [0], given: 164 Re: Marcus deposited$8,000 to open a new savings account that   [#permalink] 21 Jun 2017, 03:19
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