Last visit was: 24 Apr 2024, 02:06 It is currently 24 Apr 2024, 02:06

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Manager
Manager
Joined: 03 Apr 2013
Posts: 222
Own Kudos [?]: 239 [0]
Given Kudos: 872
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Send PM
Director
Director
Joined: 29 Jun 2017
Posts: 778
Own Kudos [?]: 396 [0]
Given Kudos: 2198
Send PM
Current Student
Joined: 19 Jan 2018
Posts: 106
Own Kudos [?]: 115 [0]
Given Kudos: 3160
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29901 [0]
Given Kudos: 799
Location: Canada
Send PM
An investor opened a money market account with a single deposit of $60 [#permalink]
Expert Reply
Top Contributor
cccmom 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%


Interest earned for the first three quarters = $125 + $130 + $145 = $400

GOAL: The total interest earned on the account for the year to be 10 percent of the initial deposit?
10% of $6000 = $600

$600 - $400 = $200
So, we want the investor to earn $200 of interest during the 4th quarter.

After the first 3 quarters, the amount in the account = $6000 + $400 = $6400

What percent of $6400 equals $200?
To find out if we need to write $200/$6400 as a percent.

200/6400 = 2/64 = 1/31 = 3/93 ≈ 3.1%

So, to earn $200 interest in the 4th quarter, we need a QUARTERLY interest rate of about ≈ 3.1%

Since the question asks for the ANNUAL interest rate, we must multiply 3.1% by 4 to get 12.4%

Answer: E
Intern
Intern
Joined: 20 May 2017
Posts: 12
Own Kudos [?]: 3 [0]
Given Kudos: 59
Send PM
Re: An investor opened a money market account with a single deposit of $60 [#permalink]
Amount = principal + interest...(formula)

10 percent of the initial deposit 6000 (principal) is 600. Therefore, the 4th quarter's amount must be 6000 + 600 = 6600.

It's given that the interest earned in the first 3 quarters = 125 + 130 + 145 = 400. Therefore, the amount at the end of the quarter must be 6000 + 400 = 6400. Please note that this amount 6400 will be the principal for the 4th quarter.
Interest needed = 6600 - 6400 = 200.
(200 / 6400) × 100 = 3.125%
Therefore, A is the best answer.

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5342
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: An investor opened a money market account with a single deposit of $60 [#permalink]
Given: 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.

Asked: 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?

First quarter: -
Principle = $6000
Interest = $125
Interest rate = $125/6000 * 12/3 * 100% = 25/3 % = 6 1/3%

Second quarter: -
Principle = $6125
Interest = $130
Interest rate = $130/6125 * 12/3 * 100% =

Third quarter: -
Principle = $6255
Interest = $145
Interest rate = $145/6255 * 12/3 * 100% =

Fourth quarter: -
Principle = $6400
Interest = $6000*10% - $400 = $200
Interest rate = $200/6400 * 12/3 * 100% = 12.5%

IMO E
Director
Director
Joined: 17 Aug 2009
Posts: 623
Own Kudos [?]: 31 [0]
Given Kudos: 21
Send PM
An investor opened a money market account with a single deposit of $60 [#permalink]
Here is a detailed solution to understand the basics - 

1st Quarter
  • P = 6000
  • CI for the 1st quarter = $125
  • CI formula = P(1+r/400)-P
  • CI = 6000(1+r/400)-6000
  • So r = 8.33% for the 1st Quarter
2nd Quarter
  • P = 6125 (as we reinvested the $125 CI from the 1st quarter)
  • CI for the 2nd quarter = $130
  • CI formula = P(1+r/400)-P
  • CI = 6125(1+r/400)-6125
  • So r = 8.48% for the 2nd  Quarter
3rd Quarter
  • P = 6125+130 = 6255 (as we reinvested $130 again)
  • CI for the 3rd quarter = $145
  • CI formula = P(1+r/400)-P
  • CI = 62551+r/400)-6255
  • So r = 9.27% for the 3rd  Quarter
4th Quarter
  • P = 6255+145 = 6400
  • CI for the 4th quarter = 10% of overall 12 months (600) - 400 (for 9 months) = 200
  • CI formula = P(1+r/400)-P
  • CI = 6400(1+r/400)-6400
  • So r = 12.5% for the 4th Quarter
A = 12.5%
GMAT Club Bot
An investor opened a money market account with a single deposit of $60 [#permalink]
   1   2 
Moderators:
Math Expert
92893 posts
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne