Question

PLEASE Help! ASAP PLZ

Answer 1

Answer:

0.57 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. David's doubling time

$\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.06125}\\\\& = & \textbf{11.317 yr}\\\end{array}$

2. Violet's doubling time

The formula for interest compounded periodically is

$FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}$

where

n = the number of payments per year

$\begin{array}{rcl}9600 & = & 4800\left (1 + \dfrac{0.065}{4} \right )^{4t}\\\\2 &= & (1 + 0.01625 )^{4t}\\& = & 1.01625^{4t}\\\ln 2& = & 4 (\ln 1.01625)\times t \\& = & 0.064478t\\t& = & \dfrac{\ln 2}{0.064478}\\\\& = & \textbf{10.750 yr}\\\end{array}$

3. David's doubling time vs Violet's

11.317 - 10.750 = 0.57 yr

It would take 0.57 yr longer for David's money to double than Violet's.