Matt invested $400 in an account that was compounded continuously. After 2years, he had $500. What was the interest rate in the account?

The continuous compounding formula is:  A  =  P · e^r·t

A  =  final amount = 500         P  =  initial amount  =  400       r  =  rate (as a decimal)      t  =  time  =  2

500  =  400e^r·2

Divide both sides by 400   --->   1.25  =  e^2r

Find the ln of both sides:   --->   ln(1.25)  =  2r

--->   r  =  ln(1.25) / 2              (calculator time)