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Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously. (Round your answers to two decimal places.)

r = 12%

 Mar 19, 2022
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1 - Compounded annually:  $2 ==$1  x  1.12^n, solve for n, where n == number of years.

2 ==1.12^n, take the log of both sides

n ==log(2) / log(1.12)

n==6.12 years.

 

2 - Compounded monthly:  $2 ==$1  x  [ 1  +  0.12/12]^n, where n==number of months.

2 ==1.01^n, take the log of both sides

n ==log(2) / log(1.01)

n ==69.66 months / 12 ==5.81 years.

 

3 - Compounded daily:   $2==$1  x  [1  +  0.12/365]^n, where n==number of days

2 ==1  x  1.00032876712^n, take the log of both sides.

n ==log(2) / log(1.00032876712)

n ==2,108.67 days / 365 ==5.78 years.

 

4 - Compounded continuously:  $2 == $1  x  e^(0.12n)

2 ==e^(0.12n), take the log of both sides

0.12n ==ln(2) ==0.69314718....

n ==0.69314718.... / 0.12 ==5.7762265 ==~5.78 years.

 Mar 19, 2022

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