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Rupees 10,000 is invested at 6% interes...

Rupees 10,000 is invested at 6% interest compounded annually. How long will it take to accumulate Rs. 20, 000 in the account?

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The correct Answer is:
12 years
Principal amount = Rs. 10,000
Rate of interest = 6%
So, amount after one year = Rs. `1.06 xx 1000`
Amount after two years = Rs. ` 1.06 xx 1.06 xx 10000`
Rs.` (1.06)^(2) xx 10000`
and so on
So, amount accumulated after n years = Rs. `(1.06)^(n) xx 10000`.
Now,` (1.06)^(n) xx 10000 = 20000`
` :. (1.06)^(n) = 2`
` rArr n log_(10)1.06 = log_(10) 2`
` rArr n = (log_(10)2)/(log_(10)1.06) = (0.30103)/(0.025306)`
` rArr log n = log 0.30103 - log 0.025306`
` =-0.5213 - (-1.5968)`
` = 1.0755`
` =11.89`
So, it will take approximately 12 years.
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