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+(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`
`(\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+(0.116)/(2))^(2\cdot n)`
`2=1.058^(2n)`
`\log _(1.058)(2)=2n`
`(\log _(1.058)(2))/(2)=n`
`n\approx6.15`

Approximately 6.15 years.