Last visit was: 18 Jul 2024, 09:31 It is currently 18 Jul 2024, 09:31
Toolkit
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

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.

# A certain investment grows at an annual interest rate of 16 percent

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94402
Own Kudos [?]: 641988 [16]
Given Kudos: 85997
Director
Joined: 26 Nov 2019
Posts: 905
Own Kudos [?]: 974 [1]
Given Kudos: 59
Location: South Africa
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6049
Own Kudos [?]: 4766 [0]
Given Kudos: 463
Location: India
GPA: 3.5
Tutor
Joined: 16 Oct 2010
Posts: 15124
Own Kudos [?]: 66712 [0]
Given Kudos: 436
Location: Pune, India
Re: A certain investment grows at an annual interest rate of 16 percent [#permalink]
Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?

(A) $$81 = 1.16^{4x}$$

(B) $$81 = 1.04^x$$

(C) $$3 = 1.16^x$$

(D) $$3 = 1.04^{4x}$$

(E) $$3 = 1.04^x$$

Are You Up For the Challenge: 700 Level Questions

Compound interest is simply successive percentage increase of r%.
If annual rate is 16%, the quarterly rate will be 4% applied 4 times in a year.
If Amount has to increase by a factor of 81, it means if principal is 1, the amount becomes 81.

$$81 = 1*[(1+ 0.4)*(1+ 0.4)*(1+ 0.4)*(1+ 0.4)]^x$$

$$3^4 = 1.04^{4x}$$

Taking the fourth root, we get

3 = 1.04^x
which we need to solve to get x.

Check this post for a discussion on successive percentage changes: https://anaprep.com/arithmetic-successi ... e-changes/
Intern
Joined: 23 Jun 2023
Posts: 8
Own Kudos [?]: 3 [1]
Given Kudos: 113
Re: A certain investment grows at an annual interest rate of 16 percent [#permalink]
1
Kudos
Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?

(A) $$81 = 1.16^{4x}$$

(B) $$81 = 1.04^x$$

(C) $$3 = 1.16^x$$

(D) $$3 = 1.04^{4x}$$

(E) $$3 = 1.04^x$$

Are You Up For the Challenge: 700 Level Questions

­The question says that the amount is increased "by" a factor of 81 and not "to" a factor 81. Isn't the total amount should be (81+1)*(Initial Amount).

Could you help explain with an example the mistake I'm making?
Math Expert
Joined: 02 Sep 2009
Posts: 94402
Own Kudos [?]: 641988 [1]
Given Kudos: 85997
A certain investment grows at an annual interest rate of 16 percent [#permalink]
1
Kudos
ssinghal087 wrote:
Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?

(A) $$81 = 1.16^{4x}$$

(B) $$81 = 1.04^x$$

(C) $$3 = 1.16^x$$

(D) $$3 = 1.04^{4x}$$

(E) $$3 = 1.04^x$$

Are You Up For the Challenge: 700 Level Questions

­The question says that the amount is increased "by" a factor of 81 and not "to" a factor 81. Isn't the total amount should be (81+1)*(Initial Amount).

Could you help explain with an example the mistake I'm making?

­"Increasing by a factor of x" means multiplying by x. For example, if 10 is increased by a factor of 5, the result is 10*5 = 50.

"Decreasing by a factor of x" means dividing by x. For example, if 10 is decreased by a factor of 5, the result is 10/5 = 2.

Hope this helps.­
A certain investment grows at an annual interest rate of 16 percent [#permalink]
Moderator:
Math Expert
94402 posts