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A college student expects to earn at least $1,000 in interest on an in

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A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 20 Aug 2016, 04:18
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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
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 26 Apr 2017, 01:30
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I used approximation here . For simple interest , 5 % rate willl give interest of 1000$ on 20000$ . When it is compounded interest rate will be marginally lower .
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 20 Aug 2016, 13:04
1
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.
Answer is A







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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 21 Aug 2016, 01:11
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.
Answer is A

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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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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 21 Aug 2016, 09:45
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.




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A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 21 Aug 2016, 09:57
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.




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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.

Experts, Please help!!
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 21 Aug 2016, 10:16
abhimahna wrote:

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.

Experts, Please help!!



Thanks Abhimahna for pointing this. I'll look for another approach.
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 21 Aug 2016, 10:29
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 \(4.91\).
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 19 Oct 2018, 11:25
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.
Answer is A







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Can anybody please elucidate the problem again? Where did we get 21,000 from?
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 19 Oct 2018, 12:21
Shrija786 wrote:
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.
Answer is A







+1 for kudos



Can anybody please elucidate the problem again? Where did we get 21,000 from?

Amount = Principal + Interest
21000 = 20000 + 1000
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 19 Oct 2018, 12:23
Can you please also explain the inequality sign?
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Re: A college student expects to earn at least $1,000 in interest on an in  [#permalink]

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New post 18 Aug 2019, 23:25
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
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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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