Answer:
0.31 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Brianna's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]
2. Adam's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
If FV is twice the PV, we can calculate the doubling time.
[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]
3. Brianna's doubling time vs Adam's
10.663 - 10.355 = 0.31 yr
It would take 0.31 yr longer for Brianna's money to double than Adam's.
