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

Redeem

An investment compounds annually at an interest rate

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

An investment compounds annually at an interest rate

by BTGmoderatorLU » Wed May 16, 2018 3:28 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

An investment compounds annually at an interest rate of 34.1%. What is the smallest investment period by which time the investment will more than triple in value?

A. 3
B. 4
C. 6
D. 9
E. 12

The OA is B.

Please, can anyone help me to solve this PS question? Thanks in advance.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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 » Wed May 16, 2018 4:14 pm
BTGmoderatorLU wrote:An investment compounds annually at an interest rate of 34.1%. What is the smallest investment period by which time the investment will more than triple in value?

A. 3
B. 4
C. 6
D. 9
E. 12
We can use fractions to solve this question.
Each year, the investment increases 34.1%
This is very close to an increase of 1/3 (33.33%)

So, if the investment increases by 1/3 each year, then each year, we can find the value of the investment by multiplying last year's value by 4/3 (this represents a 1/3 increase)

So, let's say the initial investment is $1.
We want to determine how many years it takes the investment to be worth at least $3 (triple)

Year 0: $1
Year 1: ($1)(4/3) = $4/3
Year 2: ($1)(4/3)(4/3) = $16/9 (this is less than $3)
Year 3: ($1)(4/3)(4/3)(4/3) = $64/27 (this is less than $3)
Year 4: ($1)(4/3)(4/3)(4/3)(4/3) = $256/81 (this is more than $3)

So, it takes 4 years for the investment to more than triple in value.

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Fri May 18, 2018 10:34 am
BTGmoderatorLU wrote:An investment compounds annually at an interest rate of 34.1%. What is the smallest investment period by which time the investment will more than triple in value?

A. 3
B. 4
C. 6
D. 9
E. 12

The annually compounded interest formula is A = P(1 + r)^t. Since we want to triple the value of investment, A = 3P. So we have:

3P = P(1 + 0.341)^t

Divide both sides by P, we have:

3 = (1.341)^t

Let's round the base to 1.333 = 4/3. We see that (4/3)^3 = 64/27 < 3 but (4/3)^4 = 256/81 > 3. So t must be 4.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1