Question

How long will it take money to double if it is invested at the following rates?(A) 8.7% compounded semiannually(B) 11.6% compounded semiannually(A) years(Round to two decimal places as needed.)(B) years(Round to two decimal places as needed.)

Answer 1

In the first case, 8.7% compounded semiannually we have:

$2A=A(1+\frac{0.087}{2})^{2\cdot n}$

Where A is the initial amount and n the number of years.

$2=(1+0.0435)^{2\cdot n}$$2=1.0435^{2n}$$\log _{1.0435}(2)=2n$$\frac{\log_{1.0435}(2)}{2}=n$$n\approx8.14$

Approximately 8.14 years.

And for the second case, 11.6% compounded semiannually we have:

$2A=A(1+\frac{0.116}{2})^{2\cdot n}$$2=1.058^{2n}$$\log _{1.058}(2)=2n$$\frac{\log _{1.058}(2)}{2}=n$$n\approx6.15$

Approximately 6.15 years.