Question

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.

Answer 1

`\large \boxed{\$10000.00}`

Explanation:

We can use the formula for continuously compounded interest.

`\begin{array}{rcl}A & = & Pe^(rt)\\13231.30& = & Pe^(0.035 * 8)\\& = &Pe^(0.28)\\& = & P* 1.3231298\\P & = &(13231.30)/(1.3231298)\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}`