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Donald plans to invest x dollars in a savings account that
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Updated on: 07 Jul 2013, 01:20
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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
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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.




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Re: Compounded Interest
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07 Jul 2013, 01:37
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: \(x(1+0.02)^2 x > 100\) \(x(1.02^21)>100\) \(x*0.0404>100\) \(x>\frac{100}{0.0404}\approx{2475.25}\) 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: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlmichelledepositedacertainsumofmoneyinasavings138273.htmlleonaboughta1year10000certificateofdepositthat143742.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps.




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Re: Compounded Interest
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07 Mar 2010, 00:27
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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Re: Compounded Interest
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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



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Re: Compounded Interest
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19 Aug 2009, 10:34
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.



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Re: Compounded Interest
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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.



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Re: Compounded Interest
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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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Re: Compounded Interest
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19 Aug 2009, 23:14
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



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Re: Compounded Interest
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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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Donald plans to invest x dollars in a savings account that pays intere
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21 Jul 2010, 22:34
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
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22 Jul 2010, 00:06
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 AP 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
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22 Jul 2010, 00:20
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%) => AP = P*4% Also AP = 100 => P = 100/4% = 100*100/4 = 2500
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Re: Compounded Interest
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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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Re: Compounded Interest
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Updated on: 07 Jul 2013, 04:19
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.



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Re: Donald plans to invest x dollars in a savings account that
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07 Jul 2013, 03:33
Damn..when will I stop making these silly mistakes..



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Re: Compounded Interest
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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.



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Re: Donald plans to invest x dollars in a savings account that
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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
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13 Nov 2014, 06:48
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.



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Re: Donald plans to invest x dollars in a savings account that
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13 Nov 2014, 23:40
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
\(100 = p * \frac{4}{100}\)
\(p = \frac{100*100}{4} = 2500\)



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Re: Donald plans to invest x dollars in a savings account that
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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
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