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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.)

Respuesta :

kudzordzifrancis

Answer:

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

Step-by-step explanation:

The amount in a continuously compounded account is given by:

[tex]A=Pe^{rt}[/tex]

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

We substitute these values to obtain:

[tex]A=3000e^{.055*4}[/tex]

This will evaluate to:

[tex]A=3738.23019[/tex]

Rounding to the nearest cent, we get: $3738.23

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