I have 380,000 in my bank account.  The interest rate in the account
is 5%.  How much interest will I accumulate if interest is compounded
annually over the next five years?  How much interst will I earn in my
account over the next five years with continuous compounding?

Hi,

1. The formula for calculating your interest earnings using anually compounding is:

(start amount x (interest rate^periods)) - start amount

This results in:
380,000 x 1,05^5 = 484,986.99375 - 380,000 = 104,986.99375

2. The formula for calculating your interest earnings using continuous
compounding is:

(e^(interest rate as a decimal value x periods) x start amount) - start amount 
(where e is about 2.7182)

This results in:
(2.7182^(0.05 x 5) x 380,000) - 380,000 = 107,925.98626231281594840532970042


I hope you have enough information. If you any more, please ask for a
clarification!

Thank you,
paul_b_18

Sorry to intrude on another's question but I have never heard the term
"continuous compounding".   I am familiar with "compounded daily"
(sigh) in terms of credit card interest calculations.   If "continous"
is completely different than "daily", as in very different amounts,
then please confirm with  an explicit caveat so we are all perfectly
clear.

Continuous compounding has the same mathematical basis as daily
compounding.  However, daily compounding happens 365 times a year,
whereas continuous compounding happens 'infinite' times per year.

So, continuous compounding is basically the same as daily compounding,
only it happens more often.  I have never personally seen continuous
compounding actually used in real life, but is introduced as theory in
a lot of calculus and algebra textbooks.  The actual monetary
difference between daily interest and continuous interest is
surprisingly small.  For example, $1000 @ 6% nominal invested for 1
year compounded daily ends up being $1061.831311.  Same investment
compounded continuously: $1061.836547.

Sellout,
thanks for the explanation.  I was concerned there might be  a scam.