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# Donald plans to invest x dollars in a savings account that

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Director
Joined: 05 Mar 2015
Posts: 936
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

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05 Jun 2016, 04:08
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 .
Manager
Joined: 03 Jan 2017
Posts: 132
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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12 Mar 2017, 07:24
0,08 annual interest compoinded quarterly and paid in 6 months!
so the formula would be (0,08/4)^2= 4/10^(2+2)
Intern
Joined: 09 Feb 2017
Posts: 9
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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09 Apr 2017, 14:52
Hi Bunuel,

In your equation above, x(1+.02)^2 - X> 100... where did you get the -X from? The equation for compound interest is A = P (1+r/n) ^nt. I was unaware we needed to subtract an x for the correct answer or where we even got the -X from. Could you please help?
Math Expert
Joined: 02 Sep 2009
Posts: 64125
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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09 Apr 2017, 20:53
1
mikemurawski93 wrote:
Hi Bunuel,

In your equation above, x(1+.02)^2 - X> 100... where did you get the -X from? The equation for compound interest is A = P (1+r/n) ^nt. I was unaware we needed to subtract an x for the correct answer or where we even got the -X from. Could you please help?

Approximately what amount is the minimum that Donald will need to invest to earn over \$100 in interest within 6 months?

x(1+.02)^2 is the final amount, while x(1+.02)^2 - x is the interest earned.
_________________
Manager
Joined: 14 Jun 2016
Posts: 69
Location: India
GMAT 1: 610 Q49 V21
WE: Engineering (Manufacturing)
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

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26 Aug 2017, 23:34
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.
Manager
Joined: 03 May 2014
Posts: 145
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

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08 Sep 2017, 19:50
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.
Intern
Joined: 26 Dec 2016
Posts: 30
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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22 May 2018, 04:37
Annual rate -8%, so quaterly rate 2%

As the CI is quaterly(3 months), for 6 months .. 2 times

x *102/100*102/100

x*1.02*1.02

x*1.0404

check the options by replacing x....result should be 100 more than the selected choice

option D....2500 * 1.0404 = 2601.... so interest is 101...
Intern
Joined: 04 Aug 2018
Posts: 4

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15 Sep 2018, 11:42
CI = P(1 + r/400)^2n - x
100 = x(1 + 8/(4*100))^2 - x
solve for x to get x=2500 approx.
Intern
Joined: 03 Oct 2016
Posts: 37
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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05 Aug 2019, 13:44
TheRob 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?

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

We can solve this using Answers.
if the annual rate is 8% then for 6 month it is 8/2=4%
DOnald need to earn \$100 interest then
A) 1500- 4% of 1500= \$60<100
B0 1750- 4% of 1750=\$70<100
c) 2000- 4% 0f 2000= \$80<100
d) 2500- 4% of 2000= \$100 so answer is (D)

Hope this helps..
Intern
Joined: 18 Jul 2018
Posts: 30
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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11 Jan 2020, 19:09
Sorry if this is unrelated, but where can I find the "code" or "tag" (e.g. M14-30) to this problem? I'm compiling notes on different Qs, and I'd rather not have to write the title every time.
Re: Donald plans to invest x dollars in a savings account that   [#permalink] 11 Jan 2020, 19:09

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