GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2019, 00:05

### 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

# An investment compounds annually at an interest rate of 34.1% What is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59721
An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

14 Oct 2019, 21:42
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:52) correct 42% (01:37) wrong based on 51 sessions

### HideShow timer Statistics

Competition Mode Question

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

_________________
VP
Joined: 20 Jul 2017
Posts: 1148
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

14 Oct 2019, 22:43
2
Let the initial amount = p
After 'n' years, Amount = p(1 + 34.1/100)^n = p(1.341)^n

When n = 2, Amount = 1.75p approx
When n = 4, Amount = 3.06p approx
--> n = 4

IMO Option B
Director
Joined: 18 May 2019
Posts: 554
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

14 Oct 2019, 23:03
1
For simplicity of calculation, I would approximate 34.1% to 34%.

After year 1, The total amount will be 1.34 times the invested amount
After year 2, the total amount will be 1.34*1.34 = 1.7956 approximately 1.80 times the invested amount
After year 3, the total amount will be 1.34*1.80 = 2.412, approximately 2.4 times the invested amount
After year 4, the total amount will be 1.34*2.4 = 3.216, and this is more than 3 times the invested amount.

Therefore the amount has to be invested for at least 4 years at the compound annual interest rate of 34.1% in order to just earn more than three times the invested amount.

The answer is therefore B.

PS. I would be looking forward to shorter alternatives, as this approach is not optimal in my view.
Senior Manager
Joined: 01 Mar 2019
Posts: 337
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

14 Oct 2019, 23:09
1
Initial Investment be x
Total amount = x(1.34)^y
Where y is time of investment
Above value have to become 3x
= (1.34*1.34*1.34*1.34) = 3.22x

So y have to be 4

OA:B

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

Updated on: 15 Oct 2019, 21:23
CI=p*(1+r/100)'t
so R=34.1%
P=1 target P =4
will happen
IMO B

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

Originally posted by Archit3110 on 15 Oct 2019, 00:57.
Last edited by Archit3110 on 15 Oct 2019, 21:23, edited 1 time in total.
Director
Joined: 24 Nov 2016
Posts: 971
Location: United States
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

15 Oct 2019, 04:48
1
Quote:
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

34.1% is close to 33.3% = 1/3

$$(1+1/3)^n≥3…(4/3)^n≥3$$
$$n=3…(4/3)^3=64/27<3$$
$$n=4…(4/3)^4=256/81=aprox.260/80=aprox.26/8>3$$

Answer (B)
Senior Manager
Joined: 10 Apr 2018
Posts: 281
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34
GPA: 3.3
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

15 Oct 2019, 06:26
1
Quote:
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

Let the principal amount be p and time period of investment be t.
So, 3p=p$$(1+\frac{34.1}{100})^t$$
=> 3=$$(\frac{134.1}{100})^t$$
=>3=$$(1.341)^t$$
For t=3, $$(1.341)^t$$=2.41 and for t=4, $$(1.341)^t$$=3.23
Thus, smallest investment period is 4 years.

Therefore, the correct answer is option B.
Senior Manager
Joined: 22 Feb 2018
Posts: 347
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

15 Oct 2019, 08:40
1
Imo. B

Initial investment = p, final amount (triple) = 3p, r = 34.1 % and n=?

3p = p (1+34.1/100)n
3 = (1.341)n, as p cancels out from the equation
Let's workout from answer choices to get the answer in quickest way,
Let's try, n=3, 1.3(41)*1.3 = 1.69, 1.69*1.3 = 1.6 * 1.3 = 2.xy, So, A is not the answer
Let's try, n=4, 1.34*1.34 = ~ 1.8, 1.8*1.8 = 3.xy, So, B can be answer.
Rest options are greater than 4, hence, it can satisfy the equation. But, we need smallest investment period to triple the investment. Hence, n = 4.

A. 3
B. 4
C. 6
D. 9
E. 12
_________________
Thanks in the forum can be expressed by hitting KUDOS!!!
Senior Manager
Joined: 07 Mar 2019
Posts: 460
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

15 Oct 2019, 11:11
1
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

Here Rule of 72 can be applied. The rule states that number '72' if divided by number of interest rate(34.1) would give a number of period in which the investment amount doubles. So to triple the investment amount we simply multiple the resultant number by 3/2. Hence

$$\frac{72}{34.1} * \frac{3}{2}$$ = 3.16

Since our investment period is annual, the smallest investment period is 4.

Alternatively,

Let investment = 100
Rate r = 34.1%
Initial amount = 100
Amount after 1st year = 134.1
Amount after 2nd year = 179.8
Amount after 3rd year = 241.1
Amount after 4th year = 323.3 (more than triple)

Answer B.

P.S.: In finance rule of 72 is not accurate so other measures are taken to make it as accurate as possible
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Joined: 17 Jan 2019
Posts: 127
Re: An investment compounds annually at an interest rate of 34.1% What is  [#permalink]

### Show Tags

15 Oct 2019, 19:17
1
2 times: 134.1*1.341 approximately 180
3 times: 180*1.341 is approximately 240
Therefore 4 times to get more than 300%

B
Re: An investment compounds annually at an interest rate of 34.1% What is   [#permalink] 15 Oct 2019, 19:17
Display posts from previous: Sort by

# An investment compounds annually at an interest rate of 34.1% What is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

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