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Manager  Joined: 28 Dec 2013
Posts: 65
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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mustdoit wrote:
TheRob wrote:
Sorry i posted a rate problem with the wrong title
Here you have the real problem of comound interest, I kind of have the idea but I don not know how to apply the formula

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

Lets solve it under 30 seconds...

8% compounded quarterly = 2% per quarter = 4% for half year

if 4% is 100 then 100% would be 2500.....Answer D. What say....

Hope this works !!!

if 4% is 100 then 100% would be 2500 -->> how did you get to 2500 exactly
Director  V
Joined: 05 Mar 2015
Posts: 937
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

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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  S
Joined: 03 Jan 2017
Posts: 131
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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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  B
Joined: 09 Feb 2017
Posts: 9
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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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?
Manager  S
Joined: 14 Jun 2016
Posts: 88
Location: India
WE: Engineering (Manufacturing)
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

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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.
_________________
Enjoying the journey Manager  B
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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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  B
Joined: 26 Dec 2016
Posts: 30
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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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  B
Joined: 04 Aug 2018
Posts: 4

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

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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  B
Joined: 18 Jul 2018
Posts: 30
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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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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