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m012#11

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m012#11 [#permalink] New post 26 Jul 2011, 03:04
If each year the population of the country grows by 20%, how many years will elapse before the population of the country doubles?

3
4
5
6
7

The answer given is B.

i calculated 5 yrs using the simple interest formula.
i = prt/100

here, i = p, r=20, so, t = 5yrs.

why the explanation given and this formula yields different results? why can't the simple interest formula can be used here?
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Senior Manager
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Re: m012#11 [#permalink] New post 26 Jul 2011, 05:01
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SI formula is not correct here, every year the population grown by 20% not on original but what is compounded last year... so either you have to use compound formula -

CI = P (1+\frac{r}{n})^(nt)

CI = 2P, n =1, r = 0.2,

2P =P (1+\frac{0.2}{1})^(1*t)

==> t=4

another way -

since this is simple calculation, i would just do the calculation -
initially - 100 people
1st year - 120 people
2nd year - 144 people
3rd year - 1.2*144 people
4th year = 1.44*144 ~ 210 people...
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Re: m012#11 [#permalink] New post 26 Jul 2011, 10:24
Simple interest formula is not used here because no. of people of that country is continuously vary every year.
Let population be 100. now on
1st year = 120
2nd year = 144
3rd year = 172.8
4th year = 207.36
thus it will cross the double population landmark on 4th year.
Re: m012#11   [#permalink] 26 Jul 2011, 10:24
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