Question

A promissory note will pay $60,000 at maturity 11 years from now. If you pay $27,000 for the note now, what rate compounded continuously would you earn?The investment would earn about % compounded continuously(Round to three decimal places as needed)

Answer 1

Rate is 7.259%

Step-by-step explanation:

Amoun to be earned 11 years from now = $60000

Initial pay = $27000

rate = ?

time = 11 years

number of times compounded = continously

To get the rate, we will apply continous compounding formula:

`P(t)\text{ = }P_0\text{ }e^(rt)`
`\begin{gathered} \text{where P(t) = 60000} \\ P_0\text{ = 27000} \\ t\text{ = 11} \\ \text{Substitute the values:} \\ 60000=27000e^(r*11) \end{gathered}`
`\begin{gathered} 60000=27000e^(11r) \\ \text{divide both sides by }27000\colon \\ (60000)/(27000)=(27000e^(11r))/(27000) \\ 2.2222\text{ = }e^(11r) \end{gathered}`
`\begin{gathered} \text{Take natural log of both sides:} \\ \log _e(2.2222)=log_e(e^(11r)) \\ \log _e\text{ = ln} \\ \\ \ln (2.2222)\text{ = 11r} \\ \text{dividing both sides by 11:} \\ r\text{ = }(\ln (2.2222))/(11) \end{gathered}`
`\begin{gathered} r\text{ = }(0.7985)/(11) \\ r\text{ = 0.072}59 \\ In\text{ percent = 0.07259 }*\text{ 100\%} \\ rate=\text{ 7.259\%} \\ \end{gathered}`