Question

Help!!!!

Answer 1

Answer:

0.28 yr  

Step-by-step explanation:

To find the doubling time with continuous compounding, we should look at the formula:

$FV = PVe^{rt}$

FV = future value, and

PV = present value

If FV is twice the PV, we can calculate the doubling time, t

$\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}$

1. Samuel's doubling time

$\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.055}\\\\& = & \textbf{12.603 yr}\\\end{array}$

2. Claire's doubling time

$\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.05625}\\\\& = & \textbf{12.323 yr}\\\end{array}$

3. Samuel's doubling time vs Claire's

12.603 - 12.323 = 0.28 yr

It would take 0.28 yr longer for Samuel's money to double than Claire's.