Question

Jon invests a mysterious sum of money in an account with a fixed annual interest rate at 6% compounded continuously.After 10 years, the balance in his account reaches 32,450. What was the amount of his initial investment? Show your work.

Answer 1

Given:

`\begin{gathered} rate(r)=6\% \\ time=10years \\ Amount(Balance-after-10years)=32450 \end{gathered}`

To Determine: The initial investment

Solution

The initial investment is the principal. This can calculated using the compounded continuously formula

`\begin{gathered} A=Pe^(rt) \\ A=Amount \\ P=Principal \\ r=rate \\ t=time \end{gathered}`

Substitute the given into the formula

`\begin{gathered} 32450=Pe^(0.06*10) \\ 32450=Pe^(0.6) \end{gathered}`
`\begin{gathered} P=(32450)/(e^(0.6)) \\ P=(32450)/(1.8221188) \\ P=17808.94 \end{gathered}`

Hence, the initial investment is $17,808.94