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%

Guest Mar 19, 2022

#1**+1 **

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.**

Guest Mar 19, 2022