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]

16 Jul 2012, 04:36

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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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Page: 23
Difficulty: 650

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Re: John deposited $10,000 to open a new savings account that [#permalink]

16 Jul 2012, 11:16

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]

16 Jul 2012, 12:54

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]

20 Jul 2012, 03:03

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] 20 Jul 2012, 03:03

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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

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