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

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John deposited $10,000 to open a new savings account that [#permalink] New post 16 Jul 2012, 03:36
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Question Stats:

69% (01:55) correct 31% (01:10) wrong based on 294 sessions
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
(8) $10,101
(e) $10,200
(D) $10,201
(E) $10,400

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Question: 21
Page: 23
Difficulty: 650
[Reveal] Spoiler: OA

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Re: John deposited $10,000 to open a new savings account that [#permalink] New post 16 Jul 2012, 10:16
john amount is compounded quarterly so the formula is A=P*(1+R/100)^N her p=principle R=rate of interest N=no of terms
rate of interest is 4% for a yr
so for quarter R=4/4=1%
john receive amt after 6 mnts so there are two quarter
so N=2
Amount A=P(1+R/100)^2
=10000(1+1/100)^2
=10000(1+0.01)^2
=10201
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Re: John deposited $10,000 to open a new savings account that [#permalink] New post 16 Jul 2012, 11:54
D.

SI = (P*R*T) / 100
SI after 1st Quarter: (10,000*4*3/12) /100 = 100
Principal for 2nd Quarter = 10,000+ 101 = 10100
SI after 2nd Quarter: (10,101*4*3/12) /100 = 101
Amount after 2nd Quarter (6 months) = 10100 +101 = 10,201
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Re: John deposited $10,000 to open a new savings account that [#permalink] New post 20 Jul 2012, 02:03
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SOLUTION

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
(8) $10,101
(e) $10,200
(D) $10,201
(E) $10,400

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.

Answer: D.

Hope it's clear.
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Re: John deposited $10,000 to open a new savings account that [#permalink] New post 14 Aug 2013, 01:38
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Re: John deposited $10,000 to open a new savings account that [#permalink] New post 18 Oct 2013, 11:46
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_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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: John deposited $10,000 to open a new savings account that [#permalink] New post 19 Oct 2014, 07:48
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Re: John deposited $10,000 to open a new savings account that   [#permalink] 19 Oct 2014, 07:48
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