Question

An investment of $56,000.00 earns 13% annual interest, compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 47 years? Round your answer to the nearest penny.

Future Value = $

Answer 1

Future Value = $25,218,968.05

Explanation:

To calculate the future value of an investment of $56,000 after 47 years that earns 13% annual interest compounded continuously, we can use the Continuous Compounding Interest formula:

`\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^(rt)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$e$ is Euler's number (constant).}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}`

In this case:

• P = $56,000
• r = 13% = 0.13
• t = 47 years

Substitute the values into the formula and solve for A:

`A=56000\cdot e^(0.13 \cdot 47)`

`A=56000\cdot e^(6.11)`

`A=56000\cdot 450.33871516762...`

`A=25\:218\:968.0493867...`

`A=\$25,218,968.05`

Therefore, the future value of the investment after 47 years is:

`\Large\boxed{\boxed{\textsf{Future Value}=\$25,218,968.05}}`