BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

compound interest

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Tue Sep 23, 2014 4:03 pm
by yeshuashley » Fri Sep 26, 2014 9:41 am
Saw this problem in an article on Beat the GMAT but would somebody please explain how to solve this problem? Thank you!

Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?

(A) 117%

(B) 120%

(C) 121%

(D) 135%

(E) 140%
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Fri Sep 26, 2014 10:35 am
Hi yeshuashley,

This is an interest rate question; based on it's wording, it requires the use of the compound interest formula (although you could calculate the interest every 6 months "by hand", but that would take a bit of work).

In most GMAT questions of this type, interest is calculated once per year, with the following formula:

Total = (Principal)(1 + R)^T

Principal = the initial money invested
R = Interest Rate per year
T = Number of years

So if you invested $100 at 10% compound interest for 2 years, you'd have....

($100)(1 + .1)^2
($100)(1.21)
$121 at the end of the two years.

In this question, we're calculating interest semi-annually, which means we calculate every 6 MONTHS. This changes the calculation a bit. Since we're calculating interest twice a year, we have to essentially "double the T and halve the R." This question includes one more "quirk" - the period of time is NOT in full years - it's five 6-month periods. This leads us to....

Principal = $X
R = 4%
T = 5 periods

We can TEST VALUES by picking a number for the Principal:

($100)(1.04)^5

This would be a real tedious calculation IF we didn't have the answers to work with. Since we're receiving 4% interest per period, and there are 5 periods, we know that 4%(5 periods) = 20%.....but since we're compounding the interest, the total would be a little bit more than 20%. There's only one answer here that accounts for the initial Principal and interest that is a little more than 20%.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Fri Sep 26, 2014 10:53 am
yeshuashley wrote:Saw this problem in an article on Beat the GMAT but would somebody please explain how to solve this problem? Thank you!

Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?

(A) 117%

(B) 120%

(C) 121%

(D) 135%

(E) 140%
On the GMAT:
compound interest = (simple interest) + (a little more).

Let the original investment = 100.

8% interest compounded semi-annually means that 4% is earned every 6 months.
On $100, 4% simple interest = $4.
From July 2012 to January 2015 = five 6-month intervals.
If $4 simple interest is earned during each of these five 6-month intervals, the resulting amount in January 2015 = 100 + 5*4 = $120.
Since the actual interest is compounded, the resulting amount in January 2015 must be just a bit more than $120.
Thus, the resulting amount in January 2015 must be just a bit more than 120% of the original investment.

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1