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Marcus deposited $8,000 to open a new savings account that

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Marcus deposited $8,000 to open a new savings account that [#permalink] New post 29 Feb 2012, 17:08
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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] New post 29 Feb 2012, 18:00
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] New post 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)
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Re: Compound Interest [#permalink] New post 29 Feb 2012, 22:39
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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] New post 28 May 2013, 05:31
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Re: Compound Interest [#permalink] New post 30 May 2013, 00:37
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.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Marcus deposited $8,000 to open a new savings account that [#permalink] New post 20 Jul 2014, 20:19
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Re: Marcus deposited $8,000 to open a new savings account that   [#permalink] 20 Jul 2014, 20:19
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