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%
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.
