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Difficulty:   75% (hard)

Question Stats: 52% (01:49) correct 48% (02:44) wrong based on 67 sessions

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A college student expects to earn at least $1,000 in interest on an initial investment of$20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08
Senior Manager  Joined: 23 Apr 2015
Posts: 283
Location: United States
Concentration: General Management, International Business
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Senthil1981 wrote:
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of$20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08

Formula for Total if compounded quarterly is =$$P ( 1+ r/4 ) ^4$$ for one year. Where r is in %.
So here, $$21,000 = 20,000 (1 + r/4)^4$$
= $$21/20 = 1.05 = (1 + r/4)^4$$
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
$$(1+4.21/400)^4 < 1.05$$

If $$r = 4.91, (1+4.91/400)^4 = 1.05$$. So 4.91 will give the minimum value for rate.

+1 for kudos

Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.
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Senior Manager  Joined: 23 Apr 2015
Posts: 283
Location: United States
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Senthil1981 wrote:
abhimahna wrote:
Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.

Hi Abhimahna,

I used onscreen calculator for taking twice the square root of ($$\sqrt{1.05}$$) and then solve for $$r$$. Not aware of another approach.
Share if you come across.

+1 for kudos

Sorry my friend. That is not the right approach to solve this question then.

Please note that this is a PS question and we are not going to get Onscreen calculator for the same. We need to ask/look for some other solution.

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Senior Manager  Joined: 23 Apr 2015
Posts: 283
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

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abhimahna wrote:
Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.

I tried binomial theorem and applied to first power $$(1 + x)^n = 1 + nx$$ and it gave $$r$$ as $$5%$$ and closest to $$5%$$ is $$4.91$$.
Manager  S
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Schools: Copenhagen, ESMT"19
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Senthil1981 wrote:
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of$20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08

Formula for Total if compounded quarterly is =$$P ( 1+ r/4 ) ^4$$ for one year. Where r is in %.
So here, $$21,000 = 20,000 (1 + r/4)^4$$
= $$21/20 = 1.05 = (1 + r/4)^4$$
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
$$(1+4.21/400)^4 < 1.05$$

If $$r = 4.91, (1+4.91/400)^4 = 1.05$$. So 4.91 will give the minimum value for rate.

+1 for kudos

Can anybody please elucidate the problem again? Where did we get 21,000 from?
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Joined: 14 Jun 2018
Posts: 217

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Can you please also explain the inequality sign?
SVP  P
Joined: 03 Jun 2019
Posts: 1746
Location: India
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] Show Tags HarveyKlaus wrote: A college student expects to earn at least$1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal? A) 4.91 B) 4.21 C) 5.72 D) 3.14 E) 1.08 Given: 1. A college student expects to earn at least$1,000 in interest on an initial investment of $20,000. 2. The money is invested for one year at interest compounded quarterly. Asked: What is the least annual interest rate that would achieve the goal? A college student expects to earn at least$1,000 in interest on an initial investment of $20,000. Interest rate expected =$1000/$20000 = 5% annually Let the annual interest rate that would achieve the goal of 5% annual interest rate be x% The money is invested for one year at interest compounded quarterly. $$(1 + x/4)^4 - 1 > 5%$$ $$(1+x/4)^4>1.05$$ If x=4.91% $$(1+x/4)^4 = 1.05001>1.05$$ IMO A _________________ "Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources: - Efficient Learning All you need to know about GMAT quant Tele: +91-11-40396815 Mobile : +91-9910661622 E-mail : kinshook.chaturvedi@gmail.com Re: A college student expects to earn at least$1,000 in interest on an in   [#permalink] 18 Aug 2019, 23:25
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