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Compounded Interest

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Compounded Interest [#permalink] New post 19 Aug 2009, 06:44
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Question Stats:

100% (04:04) correct 0% (00:00) wrong based on 3 sessions
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
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Re: Compounded Interest [#permalink] New post 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 [#permalink] New post 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 [#permalink] New post 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 [#permalink] New post 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 [#permalink] New post 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 [#permalink] New post 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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Re: Compounded Interest [#permalink] New post 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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Re: Compounded Interest   [#permalink] 07 Mar 2010, 00:27
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