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

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Manager
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Donald plans to invest x dollars in a savings account that [#permalink]  19 Aug 2009, 05:44
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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 [Reveal] Spoiler: OA Last edited by Bunuel on 07 Jul 2013, 00:20, edited 1 time in total. Renamed the topic, edited the question and added the OA. Manager Joined: 17 Dec 2007 Posts: 107 Followers: 0 Kudos [?]: 49 [0], given: 8 Re: Compounded Interest [#permalink] 19 Aug 2009, 08:18 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
$3000 Compound interest formula A = P ( 1+r/n)power nt given, n= 4 (quaterly);r =.08 the approach is substitution, our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%

lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530 after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500 1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$hence you can straightaway rule out 1750 2000 is again can be ruled out as approx 4% interest yeilds only 80$

2500$is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$as interest. hence answer is D Director Joined: 01 Apr 2008 Posts: 911 Schools: IIM Lucknow (IPMX) - Class of 2014 Followers: 10 Kudos [?]: 161 [1] , given: 18 Re: Compounded Interest [#permalink] 19 Aug 2009, 09:34 1 This post received KUDOS E. For CI: Final amount = Principal(1+ r/n)^nt Let principal = x, then final amount = x+100 x+100 = x[1+ 0.02]^2 x+100 = 1.04x 0.04x=100 x=2500 so if 2500 is invested CI will be exactly 100. To earn more interest more principal should be invested. So E. Manager Joined: 29 May 2008 Posts: 117 Followers: 1 Kudos [?]: 7 [0], given: 0 Re: Compounded Interest [#permalink] 19 Aug 2009, 10:57 Thank you veyr much here is the book explanation 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 In this case, x represents the unknown principal, r = 8%, n = 4 since the compounding is done quarterly, and t = .5 since the time frame in question is half a year (6 months). You can solve this problem without using compound interest. 8% interest over half a year, however that interest is compounded, is approximately 4% interest. So, to compute the principal, it's actually a very simple calculation: 100 = .04x 2500 = x The correct answer is D. Director Joined: 01 Apr 2008 Posts: 911 Schools: IIM Lucknow (IPMX) - Class of 2014 Followers: 10 Kudos [?]: 161 [0], given: 18 Re: Compounded Interest [#permalink] 19 Aug 2009, 21:20 Unfortunately I dont agree with the OE if I am understanding the question correctly. If we invest 2500, then CI will ONLY be 100. Question asks "to earn over$100" how much amount is to be invested. Considering rate of interest, number of years and everything else to be the same, the only way to earn CI>100 is to increase the Principal Amount because CI is directly proportional to Principal Amount.

On test day I would have chosen E for sure. What is the source though?
Manager
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Re: Compounded Interest [#permalink]  19 Aug 2009, 22:14
Economist wrote:
Unfortunately I dont agree with the OE if I am understanding the question correctly.

If we invest 2500, then CI will ONLY be 100.
Question asks "to earn over $100" how much amount is to be invested. Considering rate of interest, number of years and everything else to be the same, the only way to earn CI>100 is to increase the Principal Amount because CI is directly proportional to Principal Amount. On test day I would have chosen E for sure. What is the source though? For P=2500, first 3 months you earn 50$ as interest, next 3 months it will earn 51$as interest. So total 101$. I guess D should be fine
Director
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Re: Compounded Interest [#permalink]  19 Aug 2009, 22:47
Economist wrote:
E.

For CI:
Final amount = Principal(1+ r/n)^nt
Let principal = x, then final amount = x+100

x+100 = x[1+ 0.02]^2
x+100 = 1.04x
0.04x=100
x=2500

so if 2500 is invested CI will be exactly 100. To earn more interest more principal should be invested. So E.

OK. I got the problem, the reason is that I rounded off 1.02^2 in the above calculation. Precisely it is 1.0404 and then we get x= 2475. So anything >2475 will give CI >100
The .xx04 made the difference Hence, either I should be very precise and not round off for CI problems or solve via back tracking.
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Re: Compounded Interest [#permalink]  06 Mar 2010, 23:27
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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 !!!
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Manager
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Re: Compounded Interest [#permalink]  06 Jul 2013, 23:21
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.
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Nikhil

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Re: Compounded Interest [#permalink]  07 Jul 2013, 00:26
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.

Hi Nikhil,

why don't use the simple formula:

CI = P(R/N)^NT

P= x
CI = 100
N= 4
T = 1/2 = 0.5

=> P = 100/ (.08/4)^(4*0.5)
=> P = 100/ (.02)^2
=> p = 100/ (4 * 10^-4)
=> P = 10^6/4
=> P = 25,000

Last edited by arunraj on 07 Jul 2013, 03:19, edited 1 time in total.
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Re: Compounded Interest [#permalink]  07 Jul 2013, 00:37
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Expert's post
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.

Algebra:
x(1+0.02)^2 -x > 100
x(1.02^2-1)>100
x*0.0404>100
x>\frac{100}{0.0404}\approx{2475.25}

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

Annual rate of 8% compounded quarterly is approximately 4% in 6 months (a bit more).

x*0.04=100 --> x=2500.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html
michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html
leona-bought-a-1-year-10-000-certificate-of-deposit-that-143742.html

Theory:
math-number-theory-percents-91708.html

Hope it helps.
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Manager
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Re: Donald plans to invest x dollars in a savings account that [#permalink]  07 Jul 2013, 02:33
Damn..when will I stop making these silly mistakes..
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Nikhil

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Re: Compounded Interest [#permalink]  28 Nov 2013, 01:35
arunraj wrote:
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.

Hi Nikhil,

why don't use the simple formula:

CI = P(R/N)^NT

P= x
CI = 100
N= 4
T = 1/2 = 0.5

=> P = 100/ (.08/4)^(4*0.5)
=> P = 100/ (.02)^2
=> p = 100/ (4 * 10^-4)
=> P = 10^6/4
=> P = 25,000

I think you have quoted the incorrect formula for CI.
Re: Compounded Interest   [#permalink] 28 Nov 2013, 01:35
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# Donald plans to invest x dollars in a savings account that

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