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Manager  Joined: 29 May 2008
Posts: 103
Donald plans to invest x dollars in a savings account that  [#permalink]

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38 00:00

Difficulty:   45% (medium)

Question Stats: 69% (02:12) correct 31% (02:32) wrong based on 774 sessions

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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 Originally posted by TheRob on 19 Aug 2009, 06:44. 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. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 59561 Re: Compounded Interest [#permalink] ### Show Tags 9 7 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.

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Hope it helps.
Manager  Joined: 18 Feb 2010
Posts: 126
Schools: ISB

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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 !!!
##### General Discussion
Manager  Joined: 17 Dec 2007
Posts: 83

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3
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.
Director  Joined: 01 Apr 2008
Posts: 611
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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7
5
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: 103

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1
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
Director  Joined: 01 Apr 2008
Posts: 611
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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1
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? Intern  Joined: 09 Aug 2009 Posts: 33 Re: Compounded Interest [#permalink] ### Show Tags 1 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  Joined: 01 Apr 2008 Posts: 611 Name: Ronak Amin Schools: IIM Lucknow (IPMX) - Class of 2014 Re: Compounded Interest [#permalink] ### Show Tags 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. Manager  Joined: 07 Nov 2009 Posts: 219 Donald plans to invest x dollars in a savings account that pays intere [#permalink] ### Show Tags 4 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 Manager  Joined: 20 Jul 2010 Posts: 76 Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink] ### Show Tags 1 2 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 SVP  Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2478 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: Donald plans to invest x dollars in a savings account that pays intere [#permalink] ### Show Tags 4 1 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 _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Manager  Joined: 04 Dec 2011 Posts: 55 Schools: Smith '16 (I) Re: Compounded Interest [#permalink] ### Show Tags 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. Intern  Joined: 01 Jul 2013 Posts: 2 Location: United States Concentration: General Management, Strategy Schools: Insead '14, ISB '15 GPA: 4 WE: Business Development (Computer Software) Re: Compounded Interest [#permalink] ### Show Tags 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 Originally posted by arunraj on 07 Jul 2013, 01:26. Last edited by arunraj on 07 Jul 2013, 04:19, edited 1 time in total. Manager  Joined: 04 Dec 2011 Posts: 55 Schools: Smith '16 (I) Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 1 Damn..when will I stop making these silly mistakes.. Manager  Joined: 03 Dec 2012 Posts: 186 Re: Compounded Interest [#permalink] ### Show Tags 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: 19 Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 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.?
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

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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: 1727 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 2 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 $$100 = p * \frac{4}{100}$$ $$p = \frac{100*100}{4} = 2500$$ Manager  Joined: 28 Dec 2013 Posts: 65 Re: Donald plans to invest x dollars in a savings account that [#permalink] ### Show Tags 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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