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How long will it take for 20,000 to double if invested at 8% per annum and interest is compounded semi annuallly?

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Tushar Chandra eNotes educator | Certified Educator

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The amount 20000 invested at an interest rate of 8% compounded semi-annually after t years is equal to `20000*(1 + 0.04)^(2*t)` . Solve `20000*(1 + 0.04)^(2*t) = 40000` to evaluate how long it takes for the amount to double.

=> `(1.04)^(2*t) = 2`

=> `2*t*log(1.04) = log 2`

=> `t = (1/2)*(log 2)/(log 1.04)`

=> `t ~~ 8.83` years

It takes approximately 8.83 years for the amount to become double.

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olivemarie | Student

shouldn't it be 20000.(1+0.04/2)2.t with 2 representing "semi-annually"?