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### Show Tags

16 Jul 2012, 03:36
7
27
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:24) correct 27% (01:44) wrong based on 1806 sessions

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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

Diagnostic Test
Question: 21
Page: 23
Difficulty: 650

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John deposited $10,000 to open a new savings account that [#permalink] ### Show Tags 20 Jul 2012, 02:03 5 16 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.

Approach #2:

### Show Tags

16 Jul 2012, 10:16
4
2
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
##### General Discussion
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18 Oct 2013, 11:46
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18 Jul 2015, 16:15
I am new to the forum, starting on GMAT studying. I saw the solutions, but we are not using the calculator on test day so I do not understand thanks
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Re: John deposited $10,000 to open a new savings account that [#permalink] ### Show Tags 18 Jul 2015, 20:16 Amount in John's A/c after 6 months = ($10,000 * 1%) + [($10,000 * 1%) * 1%] =$10,201. Ans (D).
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### Show Tags

20 Dec 2017, 11:33
Bunuel wrote:
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

Since the account compounds quarterly, John earns 0.4/4 = 0.1 or 1 percent interest each quarter.

After Q1, he earns 10,000 x 0.01 = 100 dollars interest, and thus he has a total of 10,000 + 100 = 10,100 dollars in the account after the first quarter or the first 3 months.

After Q2, John earns another 10,100 x 0.01 = 101 dollars interest.

So, after 6 months, the total amount of money in John’s account is 10,100 + 101 = 10,201 dollars.

Alternate Solution:

We can use the compound interest formula A = P[(1 + (r/n)]^nt, with P = 10,000, r = 0.04, n = 4, and t = 0.5. Thus, we have P = 10,000[1+(0.04/4)]^2 = 10,000(1.01)^2 = 10,201.

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### Show Tags

09 Jan 2018, 17:48
Hi All,

We're told that a $10,000 investment earns 4% annual interest, compounded QUARTERLY (which means that we calculate interest 4 times per year). We're asked for the total value of the investment after 6 MONTHS. This question requires that you understand the concept behind the Compound Interest Formula (and this concept is sometimes referred to as "interest on top of interest"). If we were using SIMPLE Interest, then we'd calculate just once (and the total interest would be 4% of$10,000 = $400). However, when using Compound Interest, you calculate interest more than once per year, and you have to adjust the 'math' a bit. Based on the number of calculations that you do each year, you then have to divide the interest rate by that number of terms. Here, we calculate 4 times per year, so each interest calculation is 4%/4 = 1%. First 3 months =$10,000(1.01) = $10,100 Second 3 months =$10,100(1.01) = $10,201 Since the prompt asks for the total after 6 months, we don't have to do any additional work. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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### Show Tags

13 Jan 2018, 04:48
1
niks18 amanvermagmat Bunuel

Quote:
We can use the compound interest formula A = P[(1 + (r/n)]^nt, with P = 10,000, r = 0.04, n = 4, and t = 0.5. Thus, we have P = 10,000[1+(0.04/4)]^2 = 10,000(1.01)^2 = 10,201.

For simplification of 10,000 * $$(1.01)^2$$ is my below approach valid:

10,000 * $$(1.01)^2$$

= 101 * 101 or $$(101)^2$$ or$$(100+1)^2$$

Now using $$(a+b)^2$$ we get $$100^2 + 2 * 100 * 1 + 1^2$$ ie 10,201.

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Yes, that's correct.
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John deposited $10,000 to open a new savings account that earned [#permalink] ### Show Tags 27 Jun 2018, 18:57 hindu1988 wrote: 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 (B)$10,101
(C) $10,200 (D)$10,201
(E) $10,400 Compounded quarterly means rate is divided by 4 and time is increased four times.. So RATE :- 4/4=1 TIME :- 6 months = 1/2 year = 4*1/2=2 So Amount after 6 months = $$10000(1+\frac{1}{100})^2=10000*(\frac{101}{100})^2=101^2=10201$$ D _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor John deposited$10,000 to open a new savings account that earned &nbs [#permalink] 27 Jun 2018, 18:57
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