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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]

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19 Aug 2009, 06:44
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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, 01:20, edited 1 time in total. Renamed the topic, edited the question and added the OA. Manager Joined: 17 Dec 2007 Posts: 106 Followers: 0 Kudos [?]: 52 [0], given: 8 Re: Compounded Interest [#permalink] Show Tags 19 Aug 2009, 09:18 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: 898 Schools: IIM Lucknow (IPMX) - Class of 2014 Followers: 23 Kudos [?]: 484 [3] , given: 18 Re: Compounded Interest [#permalink] Show Tags 19 Aug 2009, 10:34 3 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: 113 Followers: 1 Kudos [?]: 72 [0], given: 0 Re: Compounded Interest [#permalink] Show Tags 19 Aug 2009, 11:57 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: 898 Schools: IIM Lucknow (IPMX) - Class of 2014 Followers: 23 Kudos [?]: 484 [0], given: 18 Re: Compounded Interest [#permalink] Show Tags 19 Aug 2009, 22:20 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?
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19 Aug 2009, 23:14
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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
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19 Aug 2009, 23:47
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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07 Mar 2010, 00:27
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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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07 Jul 2013, 00:21
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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07 Jul 2013, 01:26
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, 04:19, edited 1 time in total.
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07 Jul 2013, 01:37
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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. Answer: D. 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. _________________ Manager Joined: 04 Dec 2011 Posts: 81 Schools: Smith '16 (I) Followers: 0 Kudos [?]: 17 [1] , given: 13 Re: Donald plans to invest x dollars in a savings account that [#permalink] Show Tags 07 Jul 2013, 03:33 1 This post received KUDOS Damn..when will I stop making these silly mistakes.. _________________ Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back! 1 Kudos = 1 thanks Nikhil Senior Manager Joined: 03 Dec 2012 Posts: 367 Followers: 0 Kudos [?]: 88 [0], given: 291 Re: Compounded Interest [#permalink] Show Tags 28 Nov 2013, 02:35 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. Intern Joined: 08 Jul 2013 Posts: 20 Followers: 0 Kudos [?]: 0 [0], given: 23 Re: Donald plans to invest x dollars in a savings account that [#permalink] Show Tags 13 Nov 2014, 06:43 Hi Bunnel, Would it be correct to do the following. I used the simple interest formula. Since CI will give a greater amount than SI. an the interest is compounded quaterly. The rate for a quater would be 2% Since the duration is 6 months there would be two compounding periods.$50 per period.

so... 50= (X. 2.1)/ 100

X would be 2500.... This is SI so CI would be obviously greater.

IS this method correct.?
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Re: Donald plans to invest x dollars in a savings account that [#permalink]

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13 Nov 2014, 06:48
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vivekvijayan wrote:
Hi Bunnel,

Would it be correct to do the following.

I used the simple interest formula.
Since CI will give a greater amount than SI. an the interest is compounded quaterly. The rate for a quater would be 2%
Since the duration is 6 months there would be two compounding periods. $50 per period. so... 50= (X. 2.1)/ 100 X would be 2500.... This is SI so CI would be obviously greater. IS this method correct.? Yes, 50= x*0.02 is correct. Check other Compound Interest Problems in our Special Questions Directory. Hope it helps. _________________ SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 35 Kudos [?]: 1520 [1] , given: 193 Re: Donald plans to invest x dollars in a savings account that [#permalink] Show Tags 13 Nov 2014, 23:40 1 This post received KUDOS Answer = D = 2500 For small amount, small duration (in 6 months), with quarterly compounding, there would be hardly major difference between SI & CI. We can safely use the SI formula after proper adjustments SI = 100 Principal = p (Required to be calculated) RoI = 8% PA = 4% for 6 months $$100 = p * \frac{4}{100}$$ $$p = \frac{100*100}{4} = 2500$$ _________________ Kindly press "+1 Kudos" to appreciate GMAT Club Legend Joined: 09 Sep 2013 Posts: 9665 Followers: 465 Kudos [?]: 120 [0], given: 0 Re: Donald plans to invest x dollars in a savings account that [#permalink] Show Tags 03 Dec 2015, 03:13 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 28 Dec 2013 Posts: 79 Followers: 0 Kudos [?]: 1 [0], given: 3 Re: Donald plans to invest x dollars in a savings account that [#permalink] Show Tags 30 Jan 2016, 12:45 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
Re: Donald plans to invest x dollars in a savings account that   [#permalink] 30 Jan 2016, 12:45
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