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

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

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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. Kudos [?]: 131 [1], given: 0 Manager Joined: 17 Dec 2007 Posts: 101 Kudos [?]: 66 [0], given: 8 Re: Compounded Interest [#permalink] ### Show Tags 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 Kudos [?]: 66 [0], given: 8 Director Joined: 01 Apr 2008 Posts: 872 Kudos [?]: 884 [4], given: 18 Name: Ronak Amin Schools: IIM Lucknow (IPMX) - Class of 2014 Re: Compounded Interest [#permalink] ### Show Tags 19 Aug 2009, 09:34 4 This post received KUDOS 3 This post was BOOKMARKED 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. Kudos [?]: 884 [4], given: 18 Manager Joined: 29 May 2008 Posts: 111 Kudos [?]: 131 [0], given: 0 Re: Compounded Interest [#permalink] ### Show Tags 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. Kudos [?]: 131 [0], given: 0 Director Joined: 01 Apr 2008 Posts: 872 Kudos [?]: 884 [0], given: 18 Name: Ronak Amin Schools: IIM Lucknow (IPMX) - Class of 2014 Re: Compounded Interest [#permalink] ### Show Tags 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?

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19 Aug 2009, 22:14
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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, 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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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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Donald plans to invest x dollars in a savings account that pays intere [#permalink]

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21 Jul 2010, 21:34
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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

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

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21 Jul 2010, 23:06
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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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21 Jul 2010, 23:20
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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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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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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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07 Jul 2013, 00:37
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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. _________________ Kudos [?]: 139295 [4], given: 12783 Manager Joined: 04 Dec 2011 Posts: 80 Kudos [?]: 29 [1], given: 13 Schools: Smith '16 (I) Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 07 Jul 2013, 02:33 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 Kudos [?]: 29 [1], given: 13 Senior Manager Joined: 03 Dec 2012 Posts: 328 Kudos [?]: 198 [0], given: 291 Re: Compounded Interest [#permalink] ### Show Tags 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. Kudos [?]: 198 [0], given: 291 Intern Joined: 08 Jul 2013 Posts: 19 Kudos [?]: 3 [0], given: 23 Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 13 Nov 2014, 05:43 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, 05:48
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. _________________ Kudos [?]: 139295 [0], given: 12783 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1844 Kudos [?]: 2859 [2], given: 193 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 13 Nov 2014, 22:40 2 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 Kudos [?]: 2859 [2], given: 193 Manager Joined: 28 Dec 2013 Posts: 74 Kudos [?]: 5 [0], given: 3 Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 30 Jan 2016, 11:45 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

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Re: Donald plans to invest x dollars in a savings account that   [#permalink] 30 Jan 2016, 11:45

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