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Senior Manager
Joined: 30 May 2005
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interest [#permalink]  17 Aug 2005, 13:30
hello

Feng invests his bonus check in a bank account that pays 20%
interest, compounded annually. How many years will it take
for the initial balance in this account to double in value?

A. 2
B. 3
C. 4
D. 5
E. 6

plz shows your works and reasoning
thanks
Senior Manager
Joined: 30 May 2005
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A try [#permalink]  17 Aug 2005, 15:12
I have tried 2 approaches

P be the principal, the begining amount

compound interest interest formula (1+r/100)^n
r rate of interest

n number of period in a year here once a year

so first approach i could n 't get through
P+P((1+2O/100)^n)= 2P
p +P(6/5)^n =2 P

get stuck here
so
other approach

2p=P((1+2O/100)^n)

2p /p=(1+2O/100)^n)

2=6/5^n
n = 4
Manager
Joined: 19 Jul 2005
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Can u try like

First year=1+20%=1.2
Second year=1.2(.2)+1.2=1.44
Third year=1.44(.2)+1.44=1.728
Fourt year=1.728(.2)+1.728=2.03756

So the answer is 4. It just took one minute and 40 seconds
Manager
Joined: 14 Jul 2005
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Location: Sofia, Bulgaria
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I think that for this question Ali's approach is more efficient. You just need to do some relatively simple calculations and you are done.

Mandy, you got stuck with your first approach, because you counted the principal twice. The left side of the equation below is already greater than 2P.

P+P((1+2O/100)^n)= 2P

SVP
Joined: 03 Jan 2005
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Re: interest [#permalink]  18 Aug 2005, 06:03
Hmmm what I might do is this (especially if I'm short on time):
Write the following in the scrap paper:
1.2
1.2*1.2=1.44
1.2^3
1.2^4=1.44^2

As 1.4^2=1.96 I can be pretty sure that 1.44^2>2 So I'd pick 4 (C). If I have time I will actually do 1.44*1.44 to make sure I'm right.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Senior Manager
Joined: 29 Nov 2004
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I think the best way is using 100...

100
1 year - 120
2 year - 144
3 year - 172.8
4 year - should be over 200 so C
_________________

Fear Mediocrity, Respect Ignorance

Manager
Joined: 07 Oct 2004
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Obviously no investors around here.. It's a good thing none of us have business school aspirations!

The "rule of 72" is the quickest way. A balance earning X% annually will double in 72/X years. Lucky that it applies on this question--probably won't be so fortunate on the exam.
Manager
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eastcoaster9 wrote:
Obviously no investors around here.. It's a good thing none of us have business school aspirations!

The "rule of 72" is the quickest way. A balance earning X% annually will double in 72/X years. Lucky that it applies on this question--probably won't be so fortunate on the exam.

good one, eastcoaster
Manager
Joined: 06 Aug 2005
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Depending on the interest rate, the Rule of 72 is also known as the Rule of 70. As the rate gets infinitessimally small, it becomes the rule of 69.315

since (1+n)^(1/n) = e as n->0

And the logarithm(base e) of 2 = 0.69315
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