Question

$900 is deposited in an account with 4%

interest rate, compounded continuously.
What is the balance after 10 years?
F = $[?]

Answer 1

`\$1342.64`

Explanation:

We can represent the value
`A` of a quantity
`P` compounded continuously for
`t` years at
`r` rate of interest as:

`A = P\cdot e^(rt)`

This formula uses the mathematical constant
`e` (approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

`A = \$900 \cdot e^((0.04 \, \cdot \, 10))`

We can now solve for
`A`.

↓ simplifying
`e`'s exponent

`A = \$900 \cdot e^(0.4)`

↓ plugging into a calculator

`A \approx \$1342.64222788`

↓ rounding to the nearest cent

`\boxed{A \approx \$1342.64}`