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Donald plans to invest x dollars in a savings account that pays intere

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Senior Manager
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Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 21 Jul 2010, 22:34
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:51) correct 34% (02:25) wrong based on 134 sessions

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Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A. $1500
B. $1750
C. $2000
D. $2500
E. $3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years
[Reveal] Spoiler: OA

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Manager
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 22 Jul 2010, 00:06
1
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IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 22 Jul 2010, 00:20
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A = P(1 + r/n)nt here t =1/2 and n=4
=> A = P(1 + 8 %/4)4*(1/2)
=> A = P(1 + 2%)^2
=> A = P ( 1+ (2%)^2 + 4%) ,(2%)^2 is very small and can be ignored

=> A = P ( 1+4%) => A-P = P*4%
Also A-P = 100 => P = 100/4% = 100*100/4 = 2500
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 05 Jun 2016, 05:08
temp33 wrote:
IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D

Can anyone plz suggest why taking fractional values doesn't meet the ans as per my below solution
x(1+8/400)^2>x+100
x(51/50)^2>x+100
(26x/25)-x>100
x/25>100
x>2500
so ans must be E.

Thanks .

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Manager
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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 27 Aug 2017, 00:34
rohit8865 wrote:
temp33 wrote:
IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D

Can anyone plz suggest why taking fractional values doesn't meet the ans as per my below solution
x(1+8/400)^2>x+100
x(51/50)^2>x+100
(26x/25)-x>100
x/25>100
x>2500
so ans must be E.

Thanks .


Basically substitution is not required.
If we can calculate that the actual amount, say x turns to 1.0404 after 6 months then the actual interest is 0.0404x, which must be greater than 100.
While calculating (100/0.0404) you can realize that the value is just less than 2500.
Hence option D satisfies our condition and is the correct answer.
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Manager
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Joined: 04 May 2014
Posts: 127

Kudos [?]: 9 [0], given: 69

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Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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New post 08 Sep 2017, 20:50
We can solve this without doing complex calculation since the answer choices are wide spread.
8% is the interest compounded qtrly.
let us see if we take simple interest what are the values we get.
8% of $1500= 120 and 6-month interest will be 60. even if we take the compound interest it will not touch $100
8% of $1750=same as above no need to do the calculation or keep it to the last
8% $2000=$160 and half year or 6-month return will be 80
8% of $2500=$200 6 months return will be 100-Answer.
$3000=no need to do the calculation.

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Re: Donald plans to invest x dollars in a savings account that pays intere   [#permalink] 08 Sep 2017, 20:50
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