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Donald plans to invest x dollars in a savings account that [#permalink]
19 Aug 2009, 05:44
1
This post received KUDOS
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00:00
A
B
C
D
E
Difficulty:
45% (medium)
Question Stats:
64% (02:33) correct
36% (01:34) wrong based on 365 sessions
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?
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
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.
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?
Re: Compounded Interest [#permalink]
19 Aug 2009, 22:14
1
This post received KUDOS
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
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.
Re: Compounded Interest [#permalink]
06 Mar 2010, 23:27
8
This post received KUDOS
2
This post was BOOKMARKED
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....
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).
Re: Donald plans to invest x dollars in a savings account that [#permalink]
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.
Re: Donald plans to invest x dollars in a savings account that [#permalink]
13 Nov 2014, 05:48
Expert's post
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.
Re: Donald plans to invest x dollars in a savings account that [#permalink]
03 Dec 2015, 02:13
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Re: Donald plans to invest x dollars in a savings account that [#permalink]
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
gmatclubot
Re: Donald plans to invest x dollars in a savings account that
[#permalink]
30 Jan 2016, 11:45
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