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by ruplun » Mon Jul 05, 2010 12:35 am
Please solve this:

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
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by saurabhmahajan » Mon Jul 05, 2010 1:02 am
As from options it seems that quarterly means every 4 months

so by that calculation answer should be E: $10400.

Whats OA?
Thanks and regards,
Saurabh Mahajan

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by 4GMAT_Mumbai » Mon Jul 05, 2010 1:10 am
Hi,

I beg to differ ...

A quarter is equivalent to 3 months

The interest rate per quarter = 1%. We are interested in this as the compounding happens at the end of the quarter.

Amount at the end of 6 months = 10,000 times (1 + 0.01) times (1 + 0.01) = Rs 10,201.

In general, amount at the end of 'n' slices of 3 months each would be = 10,000 times (1.01 power n)

Hope this helps. Thanks.
Naveenan Ramachandran
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by mj78ind » Mon Jul 05, 2010 1:13 am
Using the formula

A = P(1 + r/n)^(t*n) we have P = 10,000; r = 4% ; t = 1/2 ; n = 12/3 = 4 (this one needs explaining, n is the number of time periods for which interest is calculated per annum for example quarterly = 12/3 = 2; semiannually = 12/2 = 6, to find n figure out the period after which 1st interest has to be paid and divide 12 by it).

Now A = 10000(1 + 0.04/4)^(1/2*4) = 10000(1.01)^2

Now there is a formula which is pretty neat, the formula says say we increase something by a% and then increase it again by b% then the combined increase is = a + b + a*b/100, in our case a = b = 1% (since 1.01^2 is similar to increasing the P two times by 1% each)

1% + 1% + 1*1/100 = 2.01%, hence

A = 10000(1+2.01/100) = 10000*(1.0201) = 10,201

Answer, believe me all this can be done in < 2mins :)

Cheers
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by ruplun » Mon Jul 05, 2010 2:21 am
Thanks a ton,.. the explantion and formula was quite helpful
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by Asif » Mon Jul 05, 2010 10:24 pm
I think we can solve it without any calculation if we go through the answers:

a 4% annual int. rate at the end of 6 months will be at least 2%. So the answer must be anyone of (c) or (d) but not (e) which is extreme. Now, with the term "quarterly compounding" it would be more than 2% leaving (d) to be the one answer available to be right.

I think it may save some time.
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by selango » Mon Jul 05, 2010 10:44 pm
Compounded quarterly means 1% interest for every 3 months.

Initial amount -10,000

First 3 months=10000+1/100(10000)=10100

Second 3 months=10100+1/100(10100)=10201
--Anand--
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by sreak1089 » Mon Jul 05, 2010 10:57 pm
Fairly simple.

A = P(1+R/100)^n

Compounted Quarterly => n = 2 R = 4/4 = 1%
Thus A = 10,000 (1+ 1/100) ^ 2
= 10000 * (101 * 101) / (100 * 100)
= (101 * 101) = 10201
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by rsvaishu » Tue Jul 06, 2010 6:49 am
ruplun wrote:Please solve this:

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
Answer: D

A=10000(1+0.4/4)^2

= 10201
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by inmate » Wed Oct 06, 2010 12:21 pm
mj78ind wrote:Using the formula

A = P(1 + r/n)^(t*n) we have P = 10,000; r = 4% ; t = 1/2 ; n = 12/3 = 4 (this one needs explaining, n is the number of time periods for which interest is calculated per annum for example quarterly = 12/3 = 2; semiannually = 12/2 = 6, to find n figure out the period after which 1st interest has to be paid and divide 12 by it).

Now A = 10000(1 + 0.04/4)^(1/2*4) = 10000(1.01)^2

Now there is a formula which is pretty neat, the formula says say we increase something by a% and then increase it again by b% then the combined increase is = a + b + a*b/100, in our case a = b = 1% (since 1.01^2 is similar to increasing the P two times by 1% each)

1% + 1% + 1*1/100 = 2.01%, hence

A = 10000(1+2.01/100) = 10000*(1.0201) = 10,201

Answer, believe me all this can be done in < 2mins :)

Cheers
Best answer, thankz....
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by komati_anusha » Wed Mar 02, 2016 7:59 am
Thanks everyone for solution. I want to know what concepts I need to go through for this question.
Pls reply.
Thanks.
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by Brent@GMATPrepNow » Wed Mar 02, 2016 4:34 pm
ruplun wrote:Please solve this:

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
When the number of "compounding" periods is only 2 or 3, we can just calculate the interest for each period.

4% annual interest, compounded quarterly, means that for each quarter year (3 months), we are adding an interest of 1% to the amount in the bank. We can practically do this in our head.

Initial deposit = $10,000
Interest after 3 months = 1% of $10,000 = $100
Total after 3 months = $10,000 + $100 = $10,100

From here, the NEXT 3 months will yield an additional 1% of interest
So, the interest for the next 3 months = 1% of $10,100 = $101
Total after 6 months = $10,100 + 101 = [spoiler]$10,201 = D[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Matt@VeritasPrep » Thu Mar 03, 2016 12:51 am
Another very quick approach:

If we took half of 4%, we'd have 2%, or $200 in interest. But since we compound TWICE (once after 3 months, then again after six months), we should make a little extra -- just ask my credit card company -- so the number should be a tick above $200.

$400 is way too big (... well, maybe not for my credit card company), so D is the only reasonable answer.
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