GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
A certain investment grows at an annual interest rate of 8%, compounde
[#permalink]
23 Mar 2021, 05:30
23 Mar 2021, 05:30
3
Expert Reply
15
Bookmarks
00:00
Question Stats:
42% (02:11) correct
57% (01:47) wrong based on 73 sessions
Hide Show timer Statistics
A certain investment grows at an annual interest rate of 8%, 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 16?
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: A certain investment grows at an annual interest rate of 8%, compounde
[#permalink]
23 Mar 2021, 09:32
23 Mar 2021, 09:32
5
4
Bookmarks
GeminiHeat wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
\(Amount = P [1 + \frac{R}{100n}]^{nT}\)
\(T\) = time in years
\(n\) = number of times, interest is calculated
As per the question:
\(16P = P [1 + \frac{8}{100(4)}]^{4x}\)
\(16 = [1 + \frac{2}{100}]^{4x}\)
\(16 = (1.02)^{4x}\)
\(2^4 = (1.02)^{4x}\)
\(2 = (1.02)^x\)
Hence, option B
General Discussion
Re: A certain investment grows at an annual interest rate of 8%, compounde
[#permalink]
05 Jan 2022, 19:57
05 Jan 2022, 19:57
Can someone explain how this question makes sense? Why would it matter that the interest rate is compounded quarterly when we already know the annual interest rate is 8%? Shouldn't the answer be 16=1.08^x, since x is in years? I do not think that we are allowed to assume that the 8% is convertible quarterly when it explicitly states "annual interest rate".
