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Senior Manager
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interest [#permalink] New post 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
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A try [#permalink] New post 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
BACksolve with answer
n = 4
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 [#permalink] New post 17 Aug 2005, 22:35
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
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 [#permalink] New post 17 Aug 2005, 23:19
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

Your second approach is actually your corrected first approach.
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Re: interest [#permalink] New post 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.
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 [#permalink] New post 18 Aug 2005, 07:48
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
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 [#permalink] New post 18 Aug 2005, 10:40
Obviously no investors around here.. :roll: It's a good thing none of us have business school aspirations! :wink:

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.
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 [#permalink] New post 18 Aug 2005, 11:44
eastcoaster9 wrote:
Obviously no investors around here.. :roll: It's a good thing none of us have business school aspirations! :wink:

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 :-D
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 [#permalink] New post 18 Aug 2005, 12:17
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
  [#permalink] 18 Aug 2005, 12:17
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