Question

Help!!!!

Samuel invested $7,800 in an account paying an interest rate of 5 1/2 % compounded continuously. Claire invested $7,800 in an account paying an interest rate of 5 5/8% compounded daily. To the nearest hundredth of a year, how much longer would it take for Samuel's money to double than for Claire's money to double?

Answer 1

0.28 yr

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 & = & (\ln 2)/(r) \\\end{array}`

1. Samuel's doubling time

`\begin{array}{rcl}t & = & (\ln 2)/(0.055)\\\\& = & \textbf{12.603 yr}\\\end{array}`

2. Claire's doubling time

`\begin{array}{rcl}t & = & (\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.