GMAT FOCUS QUESTION-1

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 am; Location: NY; Thanked: 28 times; Followed by:11 members

GMAT FOCUS QUESTION-1

by abhasjha » Tue Jul 15, 2014 5:56 am

An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A 3.1%
B 9.3%
C 10.0%
D 10.5%
E 12.5%

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Source: Beat The GMAT — Problem Solving | Tue Jul 15, 2014 5:56 am

riskygurpreet: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun May 04, 2014 8:27 am

by riskygurpreet » Tue Jul 15, 2014 6:20 am

CAN YOU TELL ME THE ANSWER???

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Jul 15, 2014 6:24 am

abhasjha wrote:An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A 3.1%
B 9.3%
C 10.0%
D 10.5%
E 12.5%

Total amount of interest that must be earned over the entire year = 10% of 6000 = 600.
Interest earned in the first 3 quarters = 125+130+145 = 400.
Interest that must be earned in the 4th quarter = 600-400 = 200.

Amount in the account at the end of the 3rd quarter = (principal) + (interest earned in the first 3 quarters) = 6000+400 = 6400.
We can PLUG IN THE ANSWERS, which represent the annual interest rate required to earn $200 in the 4th quarter.
Since the answer choices represent the ANNUAL interest rate, 1/4 of the implied interest will be earned in the 4th quarter.

Answer choice D: 10.5%
1/4 of (10.5% of 6400) = (1/4)(10.5/100)(6400) = (10.5)(16) = 168.
To earn $200 in the 4th quarter, a higher interest rate is required.

The correct answer is E.

Last edited by GMATGuruNY on Tue Jul 15, 2014 6:42 am, edited 2 times in total.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 15, 2014 6:25 am

abhasjha wrote:An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A 3.1%
B 9.3%
C 10.0%
D 10.5%
E 12.5%

After 3 quarters, the investment value = $6000 + $125 + $130 + $145 = $6400
We want the total interest earned on the account to be 10 percent of the initial deposit.
10% of $6000 = $600
So, we want the total interest to be $600
At the moment, the investor has received $400 in interest ($125 + $130 + $145 = $400 )
So, in the 4th quarter, the investor needs to make an additional $200 in interest.

So, what must the interest rate be to make $200 in interest from an investment currently worth $6400?
Well, $200/$6400 = 1/32 = 3.125%
So, in the 4th QUARTER, the investment must receive 3.125% interest.

The question asks us to determine the ANNUAL interest rate. So, the ANNUAL interest rate must equal (3.125%)(4) = [spoiler]12.5%[/spoiler]

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 am; Location: NY; Thanked: 28 times; Followed by:11 members

by abhasjha » Tue Jul 15, 2014 7:18 am

Thank you brent and Mitch .

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Tue Jul 15, 2014 7:25 am

abhasjha wrote:An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

A 3.1%
B 9.3%
C 10.0%
D 10.5%
E 12.5%

Amount of interest to be earned by end of 4th Quarter = 10% of $6000 = $600

Amount earned in first three quarters = 125+130+145 = $400

Remaining Amount to be earned in 4th Quarter = 600-400 = $200

But the amount after 3rd Quarter = 6000+Interest earned = 6000+400 = $6400

($6400 is the new principal as it being the case of compound Interest)
Rate of interest for earning $200 over $6400 = (200/6400)x100 = 3.125% for quarter

One year has 4 quarter therefore annual rate of interest = 3.125 x 4 = 12.5% P.A.

Answer Option E

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