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20 Aug 2016, 03:18
1
4
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:56) correct 47% (02:55) wrong based on 66 sessions

### HideShow timer Statistics

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: 302
Location: United States
WE: Engineering (Consulting)

### Show Tags

21 Aug 2016, 00:11
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.

+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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### Show Tags

21 Aug 2016, 08:57
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.

+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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### Show Tags

21 Aug 2016, 09:29
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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### Show Tags

19 Oct 2018, 10:25
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.

+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: 223

### Show Tags

19 Oct 2018, 11:23
Can you please also explain the inequality sign?