Question

Find the amount in a continuously compounded account for the following condition.

​Principal, ​$3000​; Annual interest​ rate, 5.5​%; ​time, 4 years
***The balance after 4 years is ​$___***
nothing.
​(Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as​ needed.)

Answer 1

***The balance after 4 years is ​$3738.23***

Explanation:

The amount in a continuously compounded account is given by:

`A=Pe^(rt)`

where P=$3000 is the principal, r=5.5% is the annual interest rate and t=4 years.

We substitute these values to obtain:

`A=3000e^(.055*4)`

This will evaluate to:

`A=3738.23019`

Rounding to the nearest cent, we get: $3738.23